diff --git a/src/apify/_actor.py b/src/apify/_actor.py
index bd281aff..51e7d2b6 100644
--- a/src/apify/_actor.py
+++ b/src/apify/_actor.py
@@ -2,6 +2,7 @@
 
 import asyncio
 import sys
+import warnings
 from contextlib import suppress
 from datetime import datetime, timedelta, timezone
 from functools import cached_property
@@ -827,7 +828,7 @@ async def start(
         content_type: str | None = None,
         build: str | None = None,
         memory_mbytes: int | None = None,
-        timeout: timedelta | None | Literal['RemainingTime'] = None,
+        timeout: timedelta | None | Literal['inherit', 'RemainingTime'] = None,
         wait_for_finish: int | None = None,
         webhooks: list[Webhook] | None = None,
     ) -> ActorRun:
@@ -845,8 +846,8 @@ async def start(
             memory_mbytes: Memory limit for the run, in megabytes. By default, the run uses a memory limit specified
                 in the default run configuration for the Actor.
             timeout: Optional timeout for the run, in seconds. By default, the run uses timeout specified in
-                the default run configuration for the Actor. Using `RemainingTime` will set timeout of the other Actor
-                to the time remaining from this Actor timeout.
+                the default run configuration for the Actor. Using `inherit` or `RemainingTime` will set timeout of the
+                other Actor to the time remaining from this Actor timeout.
             wait_for_finish: The maximum number of seconds the server waits for the run to finish. By default,
                 it is 0, the maximum value is 300.
             webhooks: Optional ad-hoc webhooks (https://docs.apify.com/webhooks/ad-hoc-webhooks) associated with
@@ -867,14 +868,22 @@ async def start(
         else:
             serialized_webhooks = None
 
-        if timeout == 'RemainingTime':
+        if timeout in {'inherit', 'RemainingTime'}:
+            if timeout == 'RemainingTime':
+                warnings.warn(
+                    '`RemainingTime` is deprecated and will be removed in version 4.0.0. Use `inherit` instead.',
+                    DeprecationWarning,
+                    stacklevel=2,
+                )
             actor_start_timeout = self._get_remaining_time()
         elif timeout is None:
             actor_start_timeout = None
         elif isinstance(timeout, timedelta):
             actor_start_timeout = timeout
         else:
-            raise ValueError(f'Invalid timeout {timeout!r}: expected `None`, `"RemainingTime"`, or a `timedelta`.')
+            raise ValueError(
+                f'Invalid timeout {timeout!r}: expected `None`, `"inherit"`, `"RemainingTime"`, or a `timedelta`.'
+            )
 
         api_result = await client.actor(actor_id).start(
             run_input=run_input,
@@ -931,7 +940,7 @@ async def call(
         content_type: str | None = None,
         build: str | None = None,
         memory_mbytes: int | None = None,
-        timeout: timedelta | None | Literal['RemainingTime'] = None,
+        timeout: timedelta | None | Literal['inherit', 'RemainingTime'] = None,
         webhooks: list[Webhook] | None = None,
         wait: timedelta | None = None,
         logger: logging.Logger | None | Literal['default'] = 'default',
@@ -950,8 +959,8 @@ async def call(
             memory_mbytes: Memory limit for the run, in megabytes. By default, the run uses a memory limit specified
                 in the default run configuration for the Actor.
             timeout: Optional timeout for the run, in seconds. By default, the run uses timeout specified in
-                the default run configuration for the Actor. Using `RemainingTime` will set timeout of the other Actor
-                to the time remaining from this Actor timeout.
+                the default run configuration for the Actor. Using `inherit` or `RemainingTime` will set timeout of the
+                other Actor to the time remaining from this Actor timeout.
             webhooks: Optional webhooks (https://docs.apify.com/webhooks) associated with the Actor run, which can
                 be used to receive a notification, e.g. when the Actor finished or failed. If you already have
                 a webhook set up for the Actor, you do not have to add it again here.
@@ -975,14 +984,23 @@ async def call(
         else:
             serialized_webhooks = None
 
-        if timeout == 'RemainingTime':
+        if timeout in {'inherit', 'RemainingTime'}:
+            if timeout == 'RemainingTime':
+                warnings.warn(
+                    '`RemainingTime` is deprecated and will be removed in version 4.0.0. Use `inherit` instead.',
+                    DeprecationWarning,
+                    stacklevel=2,
+                )
+
             actor_call_timeout = self._get_remaining_time()
         elif timeout is None:
             actor_call_timeout = None
         elif isinstance(timeout, timedelta):
             actor_call_timeout = timeout
         else:
-            raise ValueError(f'Invalid timeout {timeout!r}: expected `None`, `"RemainingTime"`, or a `timedelta`.')
+            raise ValueError(
+                f'Invalid timeout {timeout!r}: expected `None`, `"inherit"`, `"RemainingTime"`, or a `timedelta`.'
+            )
 
         api_result = await client.actor(actor_id).call(
             run_input=run_input,
@@ -1004,7 +1022,7 @@ async def call_task(
         *,
         build: str | None = None,
         memory_mbytes: int | None = None,
-        timeout: timedelta | None = None,
+        timeout: timedelta | None | Literal['inherit'] = None,
         webhooks: list[Webhook] | None = None,
         wait: timedelta | None = None,
         token: str | None = None,
@@ -1026,7 +1044,8 @@ async def call_task(
             memory_mbytes: Memory limit for the run, in megabytes. By default, the run uses a memory limit specified
                 in the default run configuration for the Actor.
             timeout: Optional timeout for the run, in seconds. By default, the run uses timeout specified in
-                the default run configuration for the Actor.
+                the default run configuration for the Actor. Using `inherit` will set timeout of the other Actor to the
+                time remaining from this Actor timeout.
             webhooks: Optional webhooks (https://docs.apify.com/webhooks) associated with the Actor run, which can
                 be used to receive a notification, e.g. when the Actor finished or failed. If you already have
                 a webhook set up for the Actor, you do not have to add it again here.
@@ -1047,11 +1066,20 @@ async def call_task(
         else:
             serialized_webhooks = None
 
+        if timeout == 'inherit':
+            task_call_timeout = self._get_remaining_time()
+        elif timeout is None:
+            task_call_timeout = None
+        elif isinstance(timeout, timedelta):
+            task_call_timeout = timeout
+        else:
+            raise ValueError(f'Invalid timeout {timeout!r}: expected `None`, `"inherit"`, or a `timedelta`.')
+
         api_result = await client.task(task_id).call(
             task_input=task_input,
             build=build,
             memory_mbytes=memory_mbytes,
-            timeout_secs=int(timeout.total_seconds()) if timeout is not None else None,
+            timeout_secs=int(task_call_timeout.total_seconds()) if task_call_timeout is not None else None,
             webhooks=serialized_webhooks,
             wait_secs=int(wait.total_seconds()) if wait is not None else None,
         )
@@ -1321,7 +1349,7 @@ def _get_remaining_time(self) -> timedelta | None:
             return self.configuration.timeout_at - datetime.now(tz=timezone.utc)
 
         self.log.warning(
-            'Returning `None` instead of remaining time. Using `RemainingTime` argument is only possible when the Actor'
+            'Using `inherit` or `RemainingTime` argument is only possible when the Actor'
             ' is running on the Apify platform and when the timeout for the Actor run is set. '
             f'{self.is_at_home()=}, {self.configuration.timeout_at=}'
         )
diff --git a/tests/integration/actor/test_actor_call_timeouts.py b/tests/integration/actor/test_actor_call_timeouts.py
index c60ca93a..b6c7ea9f 100644
--- a/tests/integration/actor/test_actor_call_timeouts.py
+++ b/tests/integration/actor/test_actor_call_timeouts.py
@@ -9,11 +9,11 @@
     from .conftest import MakeActorFunction, RunActorFunction
 
 
-async def test_actor_start_remaining_timeout(
+async def test_actor_start_inherit_timeout(
     make_actor: MakeActorFunction,
     run_actor: RunActorFunction,
 ) -> None:
-    """Test that correct timeout is set when using `RemainingTime` value for the `timeout` argument.
+    """Test that correct timeout is set when using `inherit` value for the `timeout` argument.
 
     In this test, one Actor starts itself again and checks that the timeout is correctly set on the second Actor run.
     Timeout should be the remaining time of the first Actor run calculated at the moment of the other Actor start."""
@@ -32,7 +32,7 @@ async def main() -> None:
             other_run_data = await Actor.call(
                 actor_id=Actor.configuration.actor_id or '',
                 run_input={'called_from_another_actor': True},
-                timeout='RemainingTime',
+                timeout='inherit',
             )
             assert other_run_data is not None
             try:
@@ -50,17 +50,17 @@ async def main() -> None:
                 # Make sure the other actor run is aborted
                 await Actor.apify_client.run(other_run_data.id).abort()
 
-    actor = await make_actor(label='remaining-timeout', main_func=main)
+    actor = await make_actor(label='inherit-timeout', main_func=main)
     run_result = await run_actor(actor)
 
     assert run_result.status == 'SUCCEEDED'
 
 
-async def test_actor_call_remaining_timeout(
+async def test_actor_call_inherit_timeout(
     make_actor: MakeActorFunction,
     run_actor: RunActorFunction,
 ) -> None:
-    """Test that correct timeout is set when using `RemainingTime` value for the `timeout` argument.
+    """Test that correct timeout is set when using `inherit` value for the `timeout` argument.
 
     In this test, one Actor starts itself again and checks that the timeout is correctly set on the second Actor run.
     Timeout should be the remaining time of the first Actor run calculated at the moment of the other Actor call."""
@@ -79,7 +79,7 @@ async def main() -> None:
             other_run_data = await Actor.call(
                 actor_id=Actor.configuration.actor_id or '',
                 run_input={'called_from_another_actor': True},
-                timeout='RemainingTime',
+                timeout='inherit',
             )
 
             assert other_run_data is not None