diff --git a/can/io/asc.py b/can/io/asc.py
index fcf8fc5e4..ad5538899 100644
--- a/can/io/asc.py
+++ b/can/io/asc.py
@@ -358,6 +358,7 @@ def __init__(
         self,
         file: StringPathLike | TextIO,
         channel: int = 1,
+        timestamps_format: str = "absolute",
         **kwargs: Any,
     ) -> None:
         """
@@ -366,7 +367,21 @@ def __init__(
                      write mode, not binary write mode.
         :param channel: a default channel to use when the message does not
                         have a channel set
+        :param timestamps_format: the format of timestamps in the header.
+                     Use ``"absolute"`` (default) so that readers can recover
+                     the original wall-clock timestamps by combining the
+                     per-message offset with the trigger-block start time.
+                     Use ``"relative"`` when only the elapsed time from the
+                     start of the recording matters and no absolute time
+                     recovery is needed.
+        :raises ValueError: if *timestamps_format* is not ``"absolute"`` or
+                            ``"relative"``
         """
+        if timestamps_format not in ("absolute", "relative"):
+            raise ValueError(
+                f"timestamps_format must be 'absolute' or 'relative', "
+                f"got {timestamps_format!r}"
+            )
         if kwargs.get("append", False):
             raise ValueError(
                 f"{self.__class__.__name__} is currently not equipped to "
@@ -375,11 +390,12 @@ def __init__(
         super().__init__(file, mode="w")
 
         self.channel = channel
+        self.timestamps_format = timestamps_format
 
         # write start of file header
         start_time = self._format_header_datetime(datetime.now())
         self.file.write(f"date {start_time}\n")
-        self.file.write("base hex  timestamps absolute\n")
+        self.file.write(f"base hex  timestamps {self.timestamps_format}\n")
         self.file.write("internal events logged\n")
 
         # the last part is written with the timestamp of the first message
diff --git a/doc/changelog.d/2022.added.md b/doc/changelog.d/2022.added.md
new file mode 100644
index 000000000..4a79c2d4e
--- /dev/null
+++ b/doc/changelog.d/2022.added.md
@@ -0,0 +1 @@
+Added `timestamps_format` parameter to `ASCWriter` to allow writing `relative` or `absolute` timestamps in the ASC file header.
diff --git a/test/logformats_test.py b/test/logformats_test.py
index f8a8de91d..de9dcf548 100644
--- a/test/logformats_test.py
+++ b/test/logformats_test.py
@@ -11,6 +11,7 @@
 
 TODO: correctly set preserves_channel and adds_default_channel
 """
+
 import locale
 import logging
 import os
@@ -680,6 +681,47 @@ def test_write(self):
 
         self.assertEqual(expected_file.read_text(), actual_file.read_text())
 
+    def test_write_timestamps_format_default_is_absolute(self):
+        """ASCWriter should write 'timestamps absolute' in the header by default."""
+        with can.ASCWriter(self.test_file_name) as writer:
+            pass
+
+        content = Path(self.test_file_name).read_text()
+        self.assertIn("timestamps absolute", content)
+
+    def test_write_timestamps_format_relative(self):
+        """ASCWriter should write 'timestamps relative' when requested."""
+        with can.ASCWriter(self.test_file_name, timestamps_format="relative") as writer:
+            pass
+
+        content = Path(self.test_file_name).read_text()
+        self.assertIn("timestamps relative", content)
+        self.assertNotIn("timestamps absolute", content)
+
+    def test_write_timestamps_format_invalid(self):
+        """ASCWriter should raise ValueError for an unsupported timestamps_format."""
+        with self.assertRaises(ValueError):
+            can.ASCWriter(self.test_file_name, timestamps_format="unix")
+
+    def test_write_relative_timestamp_roundtrip(self):
+        """Messages written with relative format round-trip with relative timestamps."""
+        msgs = [
+            can.Message(timestamp=100.0, arbitration_id=0x1, data=b"\x01"),
+            can.Message(timestamp=100.5, arbitration_id=0x2, data=b"\x02"),
+        ]
+
+        with can.ASCWriter(self.test_file_name, timestamps_format="relative") as writer:
+            for m in msgs:
+                writer.on_message_received(m)
+
+        with can.ASCReader(self.test_file_name, relative_timestamp=True) as reader:
+            result = list(reader)
+
+        self.assertEqual(len(result), len(msgs))
+        # With relative_timestamp=True timestamps are offsets from the first message
+        self.assertAlmostEqual(result[0].timestamp, 0.0, places=5)
+        self.assertAlmostEqual(result[1].timestamp, 0.5, places=5)
+
     @parameterized.expand(
         [
             (