diff --git a/Changelog b/Changelog
index ed797be3..780b58e6 100644
--- a/Changelog
+++ b/Changelog
@@ -23,6 +23,11 @@ Releases
 
  * Fixed `UnicodeDecodeError` when an archive has non-ASCII characters.
 
+ * Honor the ``SOURCE_DATE_EPOCH`` environment variable to support
+   `reproducible builds
+   <https://reproducible-builds.org/docs/source-date-epoch/>`_.
+   [#187](https://github.com/matthew-brett/delocate/pull/187)
+
 * [0.10.4] - 2022-12-17
 
   * Dependency paths with ``@rpath``, ``@loader_path`` and ``@executable_path``
diff --git a/delocate/tests/env_tools.py b/delocate/tests/env_tools.py
index 29d2cc9d..f73c4408 100644
--- a/delocate/tests/env_tools.py
+++ b/delocate/tests/env_tools.py
@@ -1,5 +1,6 @@
 import os
 from contextlib import contextmanager
+from typing import Iterator
 
 from ..tmpdirs import InTemporaryDirectory
 
@@ -24,3 +25,20 @@ def TempDirWithoutEnvVars(*env_vars):
             else:
                 if var in os.environ:
                     del os.environ[var]
+
+
+@contextmanager
+def _scope_env(**env: str) -> Iterator[None]:
+    """Add `env` to the environment and remove them after testing
+    is complete.
+    """
+    env_save = {key: os.environ.get(key) for key in env}
+    try:
+        os.environ.update(env)
+        yield
+    finally:
+        for key, value in env_save.items():
+            if value is None:
+                del os.environ[key]
+            else:
+                os.environ[key] = value
diff --git a/delocate/tests/test_wheelies.py b/delocate/tests/test_wheelies.py
index 21da2fea..fabe189d 100644
--- a/delocate/tests/test_wheelies.py
+++ b/delocate/tests/test_wheelies.py
@@ -5,6 +5,7 @@
 import stat
 import subprocess
 import sys
+import zipfile
 from glob import glob
 from os.path import abspath, basename, exists, isdir
 from os.path import join as pjoin
@@ -30,6 +31,7 @@
     zip2dir,
 )
 from ..wheeltools import InWheel
+from .env_tools import _scope_env
 from .pytest_tools import assert_equal, assert_false, assert_raises, assert_true
 from .test_install_names import DATA_PATH, EXT_LIBS
 from .test_tools import ARCH_BOTH, ARCH_M1
@@ -439,3 +441,20 @@ def test_fix_namespace() -> None:
         }
 
         assert delocate_wheel(NAMESPACE_WHEEL, "out.whl") == stray_libs
+
+
+def test_source_date_epoch() -> None:
+    with InTemporaryDirectory():
+        zip2dir(PURE_WHEEL, "package")
+        for date_time, sde in (
+            ((1980, 1, 1, 0, 0, 0), 42),
+            ((1980, 1, 1, 0, 0, 0), 315532800),
+            ((1980, 1, 1, 0, 0, 2), 315532802),
+            ((2020, 2, 2, 0, 0, 0), 1580601600),
+        ):
+            with _scope_env(SOURCE_DATE_EPOCH=str(sde)):
+                dir2zip("package", "package.zip")
+            with zipfile.ZipFile("package.zip", "r") as zip:
+                for name in zip.namelist():
+                    member = zip.getinfo(name)
+                    assert_equal(member.date_time, date_time)
diff --git a/delocate/tools.py b/delocate/tools.py
index 18b727bc..bb1d1762 100644
--- a/delocate/tools.py
+++ b/delocate/tools.py
@@ -5,6 +5,7 @@
 import re
 import stat
 import subprocess
+import time
 import warnings
 import zipfile
 from datetime import datetime
@@ -844,12 +845,42 @@ def zip2dir(
             os.utime(extracted_path, (modified_time, modified_time))
 
 
+_ZIP_TIMESTAMP_MIN = 315532800  # 1980-01-01 00:00:00 UTC
+_DateTuple = Tuple[int, int, int, int, int, int]
+
+
+def _get_zip_datetime(
+    date_time: Optional[_DateTuple] = None,
+) -> Optional[_DateTuple]:
+    """Utility function to support reproducible builds
+
+    https://reproducible-builds.org/docs/source-date-epoch/
+
+    Parameters
+    ----------
+    date_time : tuple of int, optional
+        Datetime tuple ``(Y, m, d, H, M, S)``.
+
+    Returns
+    -------
+    zip_date_time : tuple of int, optional
+        Datetime tuple corresponding to the ``SOURCE_DATE_EPOCH``
+        environment variable if set, otherwise the input `date_time`.
+    """
+    source_date_epoch = os.environ.get("SOURCE_DATE_EPOCH")
+    if source_date_epoch is not None:
+        timestamp = max(int(source_date_epoch), _ZIP_TIMESTAMP_MIN)
+        date_time = time.gmtime(timestamp)[0:6]
+    return date_time
+
+
 def dir2zip(
     in_dir: str | PathLike[str],
     zip_fname: str | PathLike[str],
     *,
     compression: int = zipfile.ZIP_DEFLATED,
     compress_level: int = -1,
+    date_time: Optional[_DateTuple] = None,
 ) -> None:
     """Make a zip file `zip_fname` with contents of directory `in_dir`
 
@@ -867,7 +898,10 @@ def dir2zip(
         The zipfile compression type used.
     compress_level : int, optional, keyword-only
         The compression level used for this archive.
+    date_time : tuple of int, optional, keyword-only
+        Datetime tuple ``(Y, m, d, H, M, S)`` for all recorded entries.
     """
+    date_time = _get_zip_datetime(date_time)
     with zipfile.ZipFile(
         zip_fname, "w", compression=compression, compresslevel=compress_level
     ) as zip:
@@ -876,11 +910,15 @@ def dir2zip(
                 dir_path = Path(root, dir)
                 out_dir_name = str(dir_path.relative_to(in_dir)) + "/"
                 zip_info = zipfile.ZipInfo.from_file(dir_path, out_dir_name)
+                if date_time is not None:
+                    zip_info.date_time = date_time
                 zip.writestr(zip_info, b"")
             for file in files:
                 file_path = Path(root, file)
                 out_file_path = file_path.relative_to(in_dir)
                 zip_info = zipfile.ZipInfo.from_file(file_path, out_file_path)
+                if date_time is not None:
+                    zip_info.date_time = date_time
                 zip.writestr(
                     zip_info,
                     file_path.read_bytes(),