diff --git a/CHANGELOG.md b/CHANGELOG.md
index 4587282..5a72637 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -3,6 +3,11 @@
 The `pycldf` package adheres to [Semantic Versioning](http://semver.org/spec/v2.0.0.html).
 
 
+## Unreleased
+
+- Make sure all local media files are copied with `Dataset.copy` as well.
+
+
 ## [1.41.0] - 2025-02-15
 
 - Added a utility function to query SQLite DBs using user-defined functions, aggregates or collations.
diff --git a/src/pycldf/dataset.py b/src/pycldf/dataset.py
index f0aa3f1..034e74d 100644
--- a/src/pycldf/dataset.py
+++ b/src/pycldf/dataset.py
@@ -957,6 +957,8 @@ def copy(self, dest: typing.Union[str, pathlib.Path], mdname: str = None) -> pat
             ...     if 'with_examples' in ds.directory.name:
             ...         ds.copy('some_directory', mdname='md.json')
         """
+        from pycldf.media import MediaTable
+
         dest = pathlib.Path(dest)
         if not dest.exists():
             dest.mkdir(parents=True)
@@ -983,6 +985,12 @@ def copy(self, dest: typing.Union[str, pathlib.Path], mdname: str = None) -> pat
         mdpath = dest.joinpath(
             mdname or  # noqa: W504
             (self.tablegroup.base.split('/')[-1] if from_url else self.tablegroup._fname.name))
+        if 'MediaTable' in self:
+            for f in MediaTable(self):
+                if f.scheme == 'file' and f.local_path().exists():
+                    target = dest / f.relpath
+                    target.parent.mkdir(parents=True, exist_ok=True)
+                    shutil.copy(f.local_path(), target)
         if from_url:
             del ds.tablegroup.at_props['base']  # pragma: no cover
         ds.write_metadata(fname=mdpath)
diff --git a/tests/test_dataset.py b/tests/test_dataset.py
index c66e386..fb6b8c9 100644
--- a/tests/test_dataset.py
+++ b/tests/test_dataset.py
@@ -14,6 +14,7 @@
     Generic, Wordlist, StructureDataset, Dictionary, ParallelText, Dataset, TextCorpus,
     GitRepository, make_column, get_modules, iter_datasets, SchemaError)
 from pycldf.sources import Sources
+from pycldf.media import MediaTable
 
 
 @pytest.fixture
@@ -925,6 +926,15 @@ def test_Dataset_copy(tmp_path):
     assert Dataset.from_metadata(tmp_path / 'moved' / 'md.json').validate()
 
 
+def test_Dataset_copy_with_media(tmp_path, dataset_with_media):
+    dataset_with_media.copy(tmp_path, mdname='md.json')
+    filecontent = {f.id: f.read() for f in MediaTable(dataset_with_media)}
+    ds = Dataset.from_metadata(tmp_path / 'md.json')
+    for i, f in enumerate(MediaTable(ds)):
+        assert f.read() == filecontent[f.id]
+    assert i > 1
+
+
 def test_Dataset_rename_column(ds):
     lt = ds.add_component('LanguageTable')
     lt.aboutUrl = URITemplate('{#ID}.md')