diff --git a/e2e/peer/peer-unavailable.html b/e2e/peer/peer-unavailable.html
new file mode 100644
index 000000000..cacf82296
--- /dev/null
+++ b/e2e/peer/peer-unavailable.html
@@ -0,0 +1,43 @@
+<!doctype html>
+<html lang="en">
+	<head>
+		<meta charset="UTF-8" />
+		<meta name="viewport" content="width=device-width, initial-scale=1.0" />
+		<title></title>
+		<link rel="stylesheet" href="../style.css" />
+	</head>
+	<body>
+		<h1>PEER-UNAVAILABLE</h1>
+		<div id="messages"></div>
+		<div id="error-message"></div>
+		<script src="/dist/peerjs.js"></script>
+		<script type="application/javascript">
+			/**
+			 * @type {typeof import("../..").Peer}
+			 */
+			const Peer = window.peerjs.Peer;
+
+			const connectionErrors = document.getElementById("messages");
+			const peerErrors = document.getElementById("error-message");
+
+			const not_existing_peer = crypto
+				.getRandomValues(new Uint8Array(16))
+				.join("");
+
+			const peer = new Peer();
+			peer
+				.once(
+					"error",
+					(error) => void (peerErrors.textContent += JSON.stringify(error)),
+				)
+				.once("open", (id) => {
+					const connection = peer.connect(not_existing_peer);
+					connection.once(
+						"error",
+						(error) =>
+							void (connectionErrors.textContent += JSON.stringify(error)),
+					);
+				});
+		</script>
+	</body>
+</html>
diff --git a/e2e/peer/peer.spec.ts b/e2e/peer/peer.spec.ts
index 7545a23ce..b593a3800 100644
--- a/e2e/peer/peer.spec.ts
+++ b/e2e/peer/peer.spec.ts
@@ -17,4 +17,9 @@ describe("Peer", () => {
 		await P.waitForMessage('{"type":"disconnected"}');
 		expect(await P.errorMessage.getText()).toBe("");
 	});
+	it("should emit an error, when the remote peer is unavailable", async () => {
+		await P.open("peer-unavailable");
+		await P.waitForMessage('{"type":"peer-unavailable"}');
+		expect(await P.errorMessage.getText()).toBe('{"type":"peer-unavailable"}');
+	});
 });
diff --git a/lib/enums.ts b/lib/enums.ts
index 0394f90aa..ee19d0cec 100644
--- a/lib/enums.ts
+++ b/lib/enums.ts
@@ -61,6 +61,7 @@ export enum PeerErrorType {
 }
 
 export enum BaseConnectionErrorType {
+	PeerUnavailable = "peer-unavailable",
 	NegotiationFailed = "negotiation-failed",
 	ConnectionClosed = "connection-closed",
 }
diff --git a/lib/peer.ts b/lib/peer.ts
index 6fa306cbc..2352ff43f 100644
--- a/lib/peer.ts
+++ b/lib/peer.ts
@@ -4,6 +4,7 @@ import { Socket } from "./socket";
 import { MediaConnection } from "./mediaconnection";
 import type { DataConnection } from "./dataconnection/DataConnection";
 import {
+	BaseConnectionErrorType,
 	ConnectionType,
 	PeerErrorType,
 	ServerMessageType,
@@ -379,6 +380,16 @@ export class Peer extends EventEmitterWithError<PeerErrorType, PeerEvents> {
 					PeerErrorType.PeerUnavailable,
 					`Could not connect to peer ${peerId}`,
 				);
+				// Emit an error on all connections with this peer.
+				const connections = (this._connections.get(peerId) ?? []).filter(
+					(c) => c.peer === peerId,
+				);
+				for (const conn of connections) {
+					conn.emitError(
+						BaseConnectionErrorType.PeerUnavailable,
+						`${peerId} is unavailable`,
+					);
+				}
 				break;
 			case ServerMessageType.Offer: {
 				// we should consider switching this to CALL/CONNECT, but this is the least breaking option.
@@ -484,7 +495,11 @@ export class Peer extends EventEmitterWithError<PeerErrorType, PeerEvents> {
 
 	/**
 	 * Connects to the remote peer specified by id and returns a data connection.
-	 * @param peer The brokering ID of the remote peer (their {@apilink Peer.id}).
+	 *
+	 * Make sure to listen to the `error` event of the resulting {@link DataConnection}
+	 * in case the connection fails.
+	 *
+	 * @param peer The brokering ID of the remote peer (their {@link Peer.id}).
 	 * @param options for specifying details about Peer Connection
 	 */
 	connect(peer: string, options: PeerConnectOption = {}): DataConnection {
