diff --git a/CHANGELOG.md b/CHANGELOG.md
index fce86fd9..96c9186d 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -11,6 +11,7 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 
 ### Changed
 
+- Rename `has_authority` condition into `server_or_singleplayer`. Old name still works, but marked as deprecated.
 - Make `ReplicatedClients::new` public.
 
 ## [0.28.1] - 2024-09-04
diff --git a/src/client/events.rs b/src/client/events.rs
index 0ea610b5..d5d2dc09 100644
--- a/src/client/events.rs
+++ b/src/client/events.rs
@@ -30,7 +30,7 @@ impl Plugin for ClientEventsPlugin {
             PostUpdate,
             (
                 Self::send.run_if(client_connected),
-                Self::resend_locally.run_if(has_authority),
+                Self::resend_locally.run_if(server_or_singleplayer),
             )
                 .chain()
                 .in_set(ClientSet::Send),
diff --git a/src/core/common_conditions.rs b/src/core/common_conditions.rs
index 5768f65d..bfb58e3e 100644
--- a/src/core/common_conditions.rs
+++ b/src/core/common_conditions.rs
@@ -10,7 +10,16 @@ pub fn server_running(server: Option<Res<RepliconServer>>) -> bool {
 /// Returns `true` if there is no client or if the existing client is disconnected.
 ///
 /// Can be used for systems that run both on the server and in singleplayer mode.
+#[deprecated(note = "Use `server_or_singleplayer`")]
 pub fn has_authority(client: Option<Res<RepliconClient>>) -> bool {
+    server_or_singleplayer(client)
+}
+
+/// Returns `true` if there is no client or if the existing client is disconnected.
+///
+/// Can be used instead of the regular [`server_running`] to seamlessly support
+/// singleplayer or listen-server mode (where server is also a player).
+pub fn server_or_singleplayer(client: Option<Res<RepliconClient>>) -> bool {
     let Some(client) = client else {
         return true;
     };
diff --git a/src/lib.rs b/src/lib.rs
index e0490c9e..5c8759ab 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -135,8 +135,8 @@ This module is also available from [`prelude`].
 
 For example, to display a "connecting" message, you can use [`client_connecting`].
 But for gameplay systems, you most likely want to run them in both server and single-player
-sessions. For example, damage registration or procedural generation systems. Use [`has_authority`]
-condition for those cases.
+sessions. For example, damage registration or procedural generation systems.
+Use [`server_or_singleplayer`] condition for those cases.
 
 If you want your systems to run only on frames when the server sends updates to clients,
 use [`ServerSet::Send`].
@@ -307,7 +307,7 @@ also as a client with ID [`ClientId::SERVER`]. So you can send such events even
 and [`FromClient`] will be emitted for them too. This way your game logic will work the same
 on client, listen server and in single-player session.
 
-For systems that receive events attach [`has_authority`] condition to receive a message
+For systems that receive events attach [`server_or_singleplayer`] condition to receive a message
 on non-client instances (server or single-player):
 
 ```
@@ -317,7 +317,7 @@ on non-client instances (server or single-player):
 # let mut app = App::new();
 # app.add_plugins(RepliconPlugins);
 app.add_client_event::<DummyEvent>(ChannelKind::Ordered)
-    .add_systems(Update, (send_events, receive_events.run_if(has_authority)));
+    .add_systems(Update, (send_events, receive_events.run_if(server_or_singleplayer)));
 
 /// Sends an event from client or listen server.
 fn send_events(mut dummy_events: EventWriter<DummyEvent>) {
@@ -383,7 +383,7 @@ from the send list):
 # let mut app = App::new();
 # app.add_plugins(RepliconPlugins);
 app.add_server_event::<DummyEvent>(ChannelKind::Ordered)
-    .add_systems(Update, (send_events.run_if(has_authority), receive_events));
+    .add_systems(Update, (send_events.run_if(server_or_singleplayer), receive_events));
 
 /// Sends an event from server or single-player.
 fn send_events(mut dummy_events: EventWriter<ToClients<DummyEvent>>) {
diff --git a/src/parent_sync.rs b/src/parent_sync.rs
index 5ae2a64a..d78f1a12 100644
--- a/src/parent_sync.rs
+++ b/src/parent_sync.rs
@@ -9,7 +9,7 @@ use serde::{Deserialize, Serialize};
 
 #[cfg(feature = "client")]
 use crate::client::ClientSet;
-use crate::core::{common_conditions::has_authority, replication_rules::AppRuleExt};
+use crate::core::{common_conditions::*, replication_rules::AppRuleExt};
 #[cfg(feature = "server")]
 use crate::server::ServerSet;
 
@@ -39,7 +39,7 @@ impl Plugin for ParentSyncPlugin {
         app.add_systems(
             PostUpdate,
             (Self::store_changes, Self::store_removals)
-                .run_if(has_authority)
+                .run_if(server_or_singleplayer)
                 .in_set(ServerSet::StoreHierarchy),
         );
     }
diff --git a/src/server/events.rs b/src/server/events.rs
index bd775ef1..d3423563 100644
--- a/src/server/events.rs
+++ b/src/server/events.rs
@@ -28,7 +28,7 @@ impl Plugin for ServerEventsPlugin {
             PostUpdate,
             (
                 Self::send.run_if(server_running),
-                Self::resend_locally.run_if(has_authority),
+                Self::resend_locally.run_if(server_or_singleplayer),
             )
                 .chain()
                 .after(ServerPlugin::send_replication)