diff --git a/fastapi/dependencies/models.py b/fastapi/dependencies/models.py
index 418c11725..62fd4cc89 100644
--- a/fastapi/dependencies/models.py
+++ b/fastapi/dependencies/models.py
@@ -22,12 +22,12 @@ class Dependant:
     security_requirements: List[SecurityRequirement] = field(default_factory=list)
     name: Optional[str] = None
     call: Optional[Callable[..., Any]] = None
-    request_param_name: Optional[str] = None
-    websocket_param_name: Optional[str] = None
-    http_connection_param_name: Optional[str] = None
-    response_param_name: Optional[str] = None
-    background_tasks_param_name: Optional[str] = None
-    security_scopes_param_name: Optional[str] = None
+    request_param_names: List[str] = field(default_factory=list)
+    websocket_param_names: List[str] = field(default_factory=list)
+    http_connection_param_names: List[str] = field(default_factory=list)
+    response_param_names: List[str] = field(default_factory=list)
+    background_tasks_param_names: List[str] = field(default_factory=list)
+    security_scopes_param_names: List[str] = field(default_factory=list)
     security_scopes: Optional[List[str]] = None
     use_cache: bool = True
     path: Optional[str] = None
diff --git a/fastapi/dependencies/utils.py b/fastapi/dependencies/utils.py
index 84dfa4d03..852ecced6 100644
--- a/fastapi/dependencies/utils.py
+++ b/fastapi/dependencies/utils.py
@@ -318,22 +318,22 @@ def add_non_field_param_to_dependency(
     *, param_name: str, type_annotation: Any, dependant: Dependant
 ) -> Optional[bool]:
     if lenient_issubclass(type_annotation, Request):
-        dependant.request_param_name = param_name
+        dependant.request_param_names.append(param_name)
         return True
     elif lenient_issubclass(type_annotation, WebSocket):
-        dependant.websocket_param_name = param_name
+        dependant.websocket_param_names.append(param_name)
         return True
     elif lenient_issubclass(type_annotation, HTTPConnection):
-        dependant.http_connection_param_name = param_name
+        dependant.http_connection_param_names.append(param_name)
         return True
     elif lenient_issubclass(type_annotation, Response):
-        dependant.response_param_name = param_name
+        dependant.response_param_names.append(param_name)
         return True
     elif lenient_issubclass(type_annotation, StarletteBackgroundTasks):
-        dependant.background_tasks_param_name = param_name
+        dependant.background_tasks_param_names.append(param_name)
         return True
     elif lenient_issubclass(type_annotation, SecurityScopes):
-        dependant.security_scopes_param_name = param_name
+        dependant.security_scopes_param_names.append(param_name)
         return True
     return None
 
@@ -670,22 +670,25 @@ async def solve_dependencies(
         )
         values.update(body_values)
         errors.extend(body_errors)
-    if dependant.http_connection_param_name:
-        values[dependant.http_connection_param_name] = request
-    if dependant.request_param_name and isinstance(request, Request):
-        values[dependant.request_param_name] = request
-    elif dependant.websocket_param_name and isinstance(request, WebSocket):
-        values[dependant.websocket_param_name] = request
-    if dependant.background_tasks_param_name:
+    for name in dependant.http_connection_param_names:
+        values[name] = request
+    if isinstance(request, Request):
+        for name in dependant.request_param_names:
+            values[name] = request
+    elif isinstance(request, WebSocket):
+        for name in dependant.websocket_param_names:
+            values[name] = request
+    if dependant.background_tasks_param_names:
         if background_tasks is None:
             background_tasks = BackgroundTasks()
-        values[dependant.background_tasks_param_name] = background_tasks
-    if dependant.response_param_name:
-        values[dependant.response_param_name] = response
-    if dependant.security_scopes_param_name:
-        values[dependant.security_scopes_param_name] = SecurityScopes(
-            scopes=dependant.security_scopes
-        )
+        for name in dependant.background_tasks_param_names:
+            values[name] = background_tasks
+    for name in dependant.response_param_names:
+        values[name] = response
+    if dependant.security_scopes_param_names:
+        security_scope = SecurityScopes(scopes=dependant.security_scopes)
+        for name in dependant.security_scopes_param_names:
+            values[name] = security_scope
     return SolvedDependency(
         values=values,
         errors=errors,
diff --git a/tests/test_duplicate_special_dependencies.py b/tests/test_duplicate_special_dependencies.py
new file mode 100644
index 000000000..8dfb57cb2
--- /dev/null
+++ b/tests/test_duplicate_special_dependencies.py
@@ -0,0 +1,61 @@
+import pytest
+from fastapi import BackgroundTasks, FastAPI, Request, Response, WebSocket
+from fastapi.security import SecurityScopes
+from fastapi.testclient import TestClient
+
+app = FastAPI()
+
+
+@app.get("/request")
+def request(r1: Request, r2: Request) -> str:
+    assert r1 is not None
+    assert r1 is r2
+    return "success"
+
+
+@app.get("/response")
+def response(r1: Response, r2: Response) -> str:
+    assert r1 is not None
+    assert r1 is r2
+    return "success"
+
+
+@app.get("/background-tasks")
+def background_tasks(t1: BackgroundTasks, t2: BackgroundTasks) -> str:
+    assert t1 is not None
+    assert t1 is t2
+    return "success"
+
+
+@app.get("/security-scopes")
+def security_scopes(sc1: SecurityScopes, sc2: SecurityScopes) -> str:
+    assert sc1 is not None
+    assert sc1 is sc2
+    return "success"
+
+
+@app.websocket("/websocket")
+async def websocket(ws1: WebSocket, ws2: WebSocket) -> str:
+    assert ws1 is ws2
+    await ws1.accept()
+    await ws1.send_text("success")
+    await ws1.close()
+
+
+@pytest.mark.parametrize(
+    "url",
+    (
+        "/request",
+        "/response",
+        "/background-tasks",
+        "/security-scopes",
+    ),
+)
+def test_duplicate_special_dependency(url: str) -> None:
+    assert TestClient(app).get(url).text == '"success"'
+
+
+def test_duplicate_websocket_dependency() -> None:
+    with TestClient(app).websocket_connect("/websocket") as ws:
+        text = ws.receive_text()
+        assert text == "success"