diff --git a/pandas/core/array_algos/datetimelike_accumulations.py b/pandas/core/array_algos/datetimelike_accumulations.py
new file mode 100644
index 0000000000000..d0c622742126b
--- /dev/null
+++ b/pandas/core/array_algos/datetimelike_accumulations.py
@@ -0,0 +1,67 @@
+"""
+datetimelke_accumulations.py is for accumulations of datetimelike extension arrays
+"""
+
+from __future__ import annotations
+
+from typing import Callable
+
+import numpy as np
+
+from pandas._libs import iNaT
+
+from pandas.core.dtypes.missing import isna
+
+
+def _cum_func(
+    func: Callable,
+    values: np.ndarray,
+    *,
+    skipna: bool = True,
+):
+    """
+    Accumulations for 1D datetimelike arrays.
+
+    Parameters
+    ----------
+    func : np.cumsum, np.maximum.accumulate, np.minimum.accumulate
+    values : np.ndarray
+        Numpy array with the values (can be of any dtype that support the
+        operation). Values is changed is modified inplace.
+    skipna : bool, default True
+        Whether to skip NA.
+    """
+    try:
+        fill_value = {
+            np.maximum.accumulate: np.iinfo(np.int64).min,
+            np.cumsum: 0,
+            np.minimum.accumulate: np.iinfo(np.int64).max,
+        }[func]
+    except KeyError:
+        raise ValueError(f"No accumulation for {func} implemented on BaseMaskedArray")
+
+    mask = isna(values)
+    y = values.view("i8")
+    y[mask] = fill_value
+
+    if not skipna:
+        mask = np.maximum.accumulate(mask)
+
+    result = func(y)
+    result[mask] = iNaT
+
+    if values.dtype.kind in ["m", "M"]:
+        return result.view(values.dtype.base)
+    return result
+
+
+def cumsum(values: np.ndarray, *, skipna: bool = True) -> np.ndarray:
+    return _cum_func(np.cumsum, values, skipna=skipna)
+
+
+def cummin(values: np.ndarray, *, skipna: bool = True):
+    return _cum_func(np.minimum.accumulate, values, skipna=skipna)
+
+
+def cummax(values: np.ndarray, *, skipna: bool = True):
+    return _cum_func(np.maximum.accumulate, values, skipna=skipna)
diff --git a/pandas/core/arrays/datetimelike.py b/pandas/core/arrays/datetimelike.py
index d735c896de901..bb21bed2dc779 100644
--- a/pandas/core/arrays/datetimelike.py
+++ b/pandas/core/arrays/datetimelike.py
@@ -121,6 +121,7 @@
     isin,
     unique1d,
 )
+from pandas.core.array_algos import datetimelike_accumulations
 from pandas.core.arraylike import OpsMixin
 from pandas.core.arrays._mixins import (
     NDArrayBackedExtensionArray,
@@ -1292,25 +1293,15 @@ def _addsub_object_array(self, other: npt.NDArray[np.object_], op):
         return res_values
 
     def _accumulate(self, name: str, *, skipna: bool = True, **kwargs):
+        if name not in {"cummin", "cummax"}:
+            raise TypeError(f"Accumulation {name} not supported for {type(self)}")
 
-        if is_period_dtype(self.dtype):
-            data = self
-        else:
-            # Incompatible types in assignment (expression has type
-            # "ndarray[Any, Any]", variable has type "DatetimeLikeArrayMixin"
-            data = self._ndarray.copy()  # type: ignore[assignment]
-
-        if name in {"cummin", "cummax"}:
-            func = np.minimum.accumulate if name == "cummin" else np.maximum.accumulate
-            result = cast(np.ndarray, nanops.na_accum_func(data, func, skipna=skipna))
-
-            # error: Unexpected keyword argument "freq" for
-            # "_simple_new" of "NDArrayBacked"  [call-arg]
-            return type(self)._simple_new(
-                result, freq=self.freq, dtype=self.dtype  # type: ignore[call-arg]
-            )
+        op = getattr(datetimelike_accumulations, name)
+        result = op(self.copy(), skipna=skipna, **kwargs)
 
-        raise TypeError(f"Accumulation {name} not supported for {type(self)}")
+        return type(self)._simple_new(
+            result, freq=None, dtype=self.dtype  # type: ignore[call-arg]
+        )
 
     @unpack_zerodim_and_defer("__add__")
     def __add__(self, other):
diff --git a/pandas/core/arrays/timedeltas.py b/pandas/core/arrays/timedeltas.py
index 9b85212336f0e..ac4e8934570ce 100644
--- a/pandas/core/arrays/timedeltas.py
+++ b/pandas/core/arrays/timedeltas.py
@@ -63,6 +63,7 @@
 from pandas.core.dtypes.missing import isna
 
 from pandas.core import nanops
+from pandas.core.array_algos import datetimelike_accumulations
 from pandas.core.arrays import datetimelike as dtl
 from pandas.core.arrays._ranges import generate_regular_range
 import pandas.core.common as com
@@ -418,12 +419,9 @@ def std(
     # Accumulations
 
     def _accumulate(self, name: str, *, skipna: bool = True, **kwargs):
-
-        data = self._ndarray.copy()
-
         if name == "cumsum":
-            func = np.cumsum
-            result = cast(np.ndarray, nanops.na_accum_func(data, func, skipna=skipna))
+            op = getattr(datetimelike_accumulations, name)
+            result = op(self._ndarray.copy(), skipna=skipna, **kwargs)
 
             return type(self)._simple_new(result, freq=None, dtype=self.dtype)
         elif name == "cumprod":
diff --git a/pandas/core/nanops.py b/pandas/core/nanops.py
index f9c6465cd948e..3efbdb4fbbf3b 100644
--- a/pandas/core/nanops.py
+++ b/pandas/core/nanops.py
@@ -1711,53 +1711,11 @@ def na_accum_func(values: ArrayLike, accum_func, *, skipna: bool) -> ArrayLike:
         np.minimum.accumulate: (np.inf, np.nan),
     }[accum_func]
 
-    # We will be applying this function to block values
-    if values.dtype.kind in ["m", "M"]:
-        # GH#30460, GH#29058
-        # numpy 1.18 started sorting NaTs at the end instead of beginning,
-        #  so we need to work around to maintain backwards-consistency.
-        orig_dtype = values.dtype
-
-        # We need to define mask before masking NaTs
-        mask = isna(values)
-
-        y = values.view("i8")
-        # Note: the accum_func comparison fails as an "is" comparison
-        changed = accum_func == np.minimum.accumulate
-
-        try:
-            if changed:
-                y[mask] = lib.i8max
+    # This should go through ea interface
+    assert values.dtype.kind not in ["m", "M"]
 
-            result = accum_func(y, axis=0)
-        finally:
-            if changed:
-                # restore NaT elements
-                y[mask] = iNaT
-
-        if skipna:
-            result[mask] = iNaT
-        elif accum_func == np.minimum.accumulate:
-            # Restore NaTs that we masked previously
-            nz = (~np.asarray(mask)).nonzero()[0]
-            if len(nz):
-                # everything up to the first non-na entry stays NaT
-                result[: nz[0]] = iNaT
-
-        if isinstance(values.dtype, np.dtype):
-            result = result.view(orig_dtype)
-        else:
-            # DatetimeArray/TimedeltaArray
-            # TODO: have this case go through a DTA method?
-            # For DatetimeTZDtype, view result as M8[ns]
-            npdtype = orig_dtype if isinstance(orig_dtype, np.dtype) else "M8[ns]"
-            # Item "type" of "Union[Type[ExtensionArray], Type[ndarray[Any, Any]]]"
-            # has no attribute "_simple_new"
-            result = type(values)._simple_new(  # type: ignore[union-attr]
-                result.view(npdtype), dtype=orig_dtype
-            )
-
-    elif skipna and not issubclass(values.dtype.type, (np.integer, np.bool_)):
+    # We will be applying this function to block values
+    if skipna and not issubclass(values.dtype.type, (np.integer, np.bool_)):
         vals = values.copy()
         mask = isna(vals)
         vals[mask] = mask_a
diff --git a/pandas/tests/arrays/datetimes/test_cumulative.py b/pandas/tests/arrays/datetimes/test_cumulative.py
new file mode 100644
index 0000000000000..ca9760d58770a
--- /dev/null
+++ b/pandas/tests/arrays/datetimes/test_cumulative.py
@@ -0,0 +1,46 @@
+import pytest
+
+import pandas._testing as tm
+from pandas.core.arrays import DatetimeArray
+
+
+class TestAccumulator:
+    def test_accumulators_freq(self):
+        # GH#50297
+        arr = DatetimeArray._from_sequence_not_strict(
+            [
+                "2000-01-01",
+                "2000-01-02",
+                "2000-01-03",
+            ],
+            freq="D",
+        )
+        result = arr._accumulate("cummin")
+        expected = DatetimeArray._from_sequence_not_strict(
+            ["2000-01-01"] * 3, freq=None
+        )
+        tm.assert_datetime_array_equal(result, expected)
+
+        result = arr._accumulate("cummax")
+        expected = DatetimeArray._from_sequence_not_strict(
+            [
+                "2000-01-01",
+                "2000-01-02",
+                "2000-01-03",
+            ],
+            freq=None,
+        )
+        tm.assert_datetime_array_equal(result, expected)
+
+    @pytest.mark.parametrize("func", ["cumsum", "cumprod"])
+    def test_accumulators_disallowed(self, func):
+        # GH#50297
+        arr = DatetimeArray._from_sequence_not_strict(
+            [
+                "2000-01-01",
+                "2000-01-02",
+            ],
+            freq="D",
+        )
+        with pytest.raises(TypeError, match=f"Accumulation {func}"):
+            arr._accumulate(func)
diff --git a/pandas/tests/arrays/timedeltas/test_cumulative.py b/pandas/tests/arrays/timedeltas/test_cumulative.py
new file mode 100644
index 0000000000000..b321dc05bef27
--- /dev/null
+++ b/pandas/tests/arrays/timedeltas/test_cumulative.py
@@ -0,0 +1,19 @@
+import pytest
+
+import pandas._testing as tm
+from pandas.core.arrays import TimedeltaArray
+
+
+class TestAccumulator:
+    def test_accumulators_disallowed(self):
+        # GH#50297
+        arr = TimedeltaArray._from_sequence_not_strict(["1D", "2D"])
+        with pytest.raises(TypeError, match="cumprod not supported"):
+            arr._accumulate("cumprod")
+
+    def test_cumsum(self):
+        # GH#50297
+        arr = TimedeltaArray._from_sequence_not_strict(["1D", "2D"])
+        result = arr._accumulate("cumsum")
+        expected = TimedeltaArray._from_sequence_not_strict(["1D", "3D"])
+        tm.assert_timedelta_array_equal(result, expected)
diff --git a/pandas/tests/series/test_cumulative.py b/pandas/tests/series/test_cumulative.py
index 6fbc78bf3ff0f..4c5fd2d44e4f4 100644
--- a/pandas/tests/series/test_cumulative.py
+++ b/pandas/tests/series/test_cumulative.py
@@ -70,12 +70,12 @@ def test_cummin_cummax(self, datetime_series, method):
             [
                 "cummax",
                 False,
-                ["NaT", "2 days", "2 days", "2 days", "2 days", "3 days"],
+                ["NaT", "NaT", "NaT", "NaT", "NaT", "NaT"],
             ],
             [
                 "cummin",
                 False,
-                ["NaT", "2 days", "2 days", "1 days", "1 days", "1 days"],
+                ["NaT", "NaT", "NaT", "NaT", "NaT", "NaT"],
             ],
         ],
     )
@@ -91,6 +91,26 @@ def test_cummin_cummax_datetimelike(self, ts, method, skipna, exp_tdi):
         result = getattr(ser, method)(skipna=skipna)
         tm.assert_series_equal(expected, result)
 
+    @pytest.mark.parametrize(
+        "func, exp",
+        [
+            ("cummin", pd.Period("2012-1-1", freq="D")),
+            ("cummax", pd.Period("2012-1-2", freq="D")),
+        ],
+    )
+    def test_cummin_cummax_period(self, func, exp):
+        # GH#28385
+        ser = pd.Series(
+            [pd.Period("2012-1-1", freq="D"), pd.NaT, pd.Period("2012-1-2", freq="D")]
+        )
+        result = getattr(ser, func)(skipna=False)
+        expected = pd.Series([pd.Period("2012-1-1", freq="D"), pd.NaT, pd.NaT])
+        tm.assert_series_equal(result, expected)
+
+        result = getattr(ser, func)(skipna=True)
+        expected = pd.Series([pd.Period("2012-1-1", freq="D"), pd.NaT, exp])
+        tm.assert_series_equal(result, expected)
+
     @pytest.mark.parametrize(
         "arg",
         [