diff --git a/rest_framework/apps.py b/rest_framework/apps.py
index f6013eb7e..9298c4bf5 100644
--- a/rest_framework/apps.py
+++ b/rest_framework/apps.py
@@ -8,3 +8,4 @@ class RestFrameworkConfig(AppConfig):
     def ready(self):
         # Add System checks
         from .checks import pagination_system_check  # NOQA
+        from .checks import www_authenticate_behavior_setting_check  # NOQA
diff --git a/rest_framework/checks.py b/rest_framework/checks.py
index d5d77bc59..12c75db3c 100644
--- a/rest_framework/checks.py
+++ b/rest_framework/checks.py
@@ -1,4 +1,4 @@
-from django.core.checks import Tags, Warning, register
+from django.core.checks import Tags, Error, Warning, register
 
 
 @register(Tags.compatibility)
@@ -19,3 +19,22 @@ def pagination_system_check(app_configs, **kwargs):
             )
         )
     return errors
+
+
+@register(Tags.compatibility)
+def www_authenticate_behavior_setting_check(app_configs, **kwargs):
+    errors = []
+    # WWW_AUTHENTICATE_BEHAVIOR setting must be 'first' or 'all'
+    from rest_framework.settings import api_settings
+    setting = api_settings.WWW_AUTHENTICATE_BEHAVIOR
+    if setting not in ['first', 'all']:
+        errors.append(
+            Error(
+                "The rest_framework setting WWW_AUTHENTICATE_BEHAVIOR must be either "
+                f"'first' or 'all' (it is currently set to '{setting}').",
+                hint="Set WWW_AUTHENTICATE_BEHAVIOR to either 'first' or 'all', "
+                     "or leave it unset (the default value is 'first').",
+                id="rest_framework.E001",
+            )
+        )
+    return errors