diff --git a/lib/mint/http.ex b/lib/mint/http.ex
index 05ee649c..45d65f78 100644
--- a/lib/mint/http.ex
+++ b/lib/mint/http.ex
@@ -287,6 +287,15 @@ defmodule Mint.HTTP do
   uses TLS and the TLS session to the host is nested inside it. *HTTPS proxies
   for HTTPS connections are available since v1.10.0*.
 
+  The `opts` in the `:proxy` tuple are the options of the connection to the proxy
+  itself and support the same options as `connect/4`. Tunnel proxies additionally
+  support:
+
+    * `:tunnel_timeout` - the maximum time (in milliseconds) to wait for the proxy
+      to reply to the `CONNECT` request. If the tunnel is not established within
+      this time, `connect/4` returns a `Mint.HTTPError` with reason
+      `{:proxy, :tunnel_timeout}`. Defaults to `30_000` (30 seconds).
+
   ## Transport options
 
   The options specified in `:transport_opts` are passed to the module that
diff --git a/lib/mint/tunnel_proxy.ex b/lib/mint/tunnel_proxy.ex
index f2e3c012..55b95fb8 100644
--- a/lib/mint/tunnel_proxy.ex
+++ b/lib/mint/tunnel_proxy.ex
@@ -56,7 +56,7 @@ defmodule Mint.TunnelProxy do
   end
 
   defp receive_response(conn, ref, timeout_deadline) do
-    timeout = timeout_deadline - System.monotonic_time(:millisecond)
+    timeout = max(timeout_deadline - System.monotonic_time(:millisecond), 0)
     socket = HTTP1.get_socket(conn)
 
     receive do
diff --git a/test/mint/tunnel_proxy_connect_test.exs b/test/mint/tunnel_proxy_connect_test.exs
index 1cb68f04..74d93aa2 100644
--- a/test/mint/tunnel_proxy_connect_test.exs
+++ b/test/mint/tunnel_proxy_connect_test.exs
@@ -37,6 +37,24 @@ defmodule Mint.TunnelProxyConnectTest do
     assert merge_body(rest, request) == "hello"
   end
 
+  test "a proxy that stalls the CONNECT response yields a tunnel timeout error" do
+    proxy_port = start_silent_proxy()
+
+    assert {:error, %Mint.HTTPError{reason: {:proxy, :tunnel_timeout}}} =
+             HTTP.connect(:https, "localhost", 443,
+               proxy: {:http, "localhost", proxy_port, [tunnel_timeout: 50]}
+             )
+  end
+
+  test "an already-elapsed tunnel deadline yields a tunnel timeout error instead of crashing" do
+    proxy_port = start_silent_proxy()
+
+    assert {:error, %Mint.HTTPError{reason: {:proxy, :tunnel_timeout}}} =
+             HTTP.connect(:https, "localhost", 443,
+               proxy: {:http, "localhost", proxy_port, [tunnel_timeout: -1]}
+             )
+  end
+
   test "IPv6 address targets produce a bracketed CONNECT authority" do
     {proxy_port, proxy_ref} = start_capturing_proxy()
 
@@ -82,6 +100,25 @@ defmodule Mint.TunnelProxyConnectTest do
     {port, ref}
   end
 
+  # Starts a one-shot proxy that accepts a single connection and never
+  # responds.
+  defp start_silent_proxy do
+    {:ok, listen_socket} =
+      :gen_tcp.listen(0, mode: :binary, packet: :raw, active: false, reuseaddr: true)
+
+    {:ok, port} = :inet.port(listen_socket)
+
+    spawn_link(fn ->
+      {:ok, socket} = :gen_tcp.accept(listen_socket)
+
+      receive do
+        :stop -> :gen_tcp.close(socket)
+      end
+    end)
+
+    port
+  end
+
   # Starts a one-shot server that accepts a single connection, reports the raw
   # request head to the test process, and closes the connection.
   defp start_capturing_proxy do