diff --git a/include/exec/libdispatch_queue.hpp b/include/exec/libdispatch_queue.hpp
index 5f717cacf..1c9bb6065 100644
--- a/include/exec/libdispatch_queue.hpp
+++ b/include/exec/libdispatch_queue.hpp
@@ -117,6 +117,8 @@ namespace experimental::execution
 
   struct libdispatch_scheduler
   {
+    using scheduler_concept = STDEXEC::scheduler_tag;
+
     bool operator==(libdispatch_scheduler const &) const = default;
 
     struct domain
diff --git a/include/exec/linux/io_uring_context.hpp b/include/exec/linux/io_uring_context.hpp
index 011cf1fb6..1ebc197d5 100644
--- a/include/exec/linux/io_uring_context.hpp
+++ b/include/exec/linux/io_uring_context.hpp
@@ -1226,6 +1226,8 @@ namespace experimental::execution
     class __scheduler
     {
      public:
+      using scheduler_concept = STDEXEC::scheduler_tag;
+
       __context* __context_;
 
       auto operator==(__scheduler const &) const -> bool = default;
diff --git a/include/exec/reschedule.hpp b/include/exec/reschedule.hpp
index 51b30d3c6..736e90f01 100644
--- a/include/exec/reschedule.hpp
+++ b/include/exec/reschedule.hpp
@@ -48,6 +48,8 @@ namespace experimental::execution
 
     struct __scheduler
     {
+      using scheduler_concept = scheduler_tag;
+
       struct __sender
       {
         using sender_concept = sender_tag;
diff --git a/include/exec/static_thread_pool.hpp b/include/exec/static_thread_pool.hpp
index 1dcee0aa0..8946b59bc 100644
--- a/include/exec/static_thread_pool.hpp
+++ b/include/exec/static_thread_pool.hpp
@@ -341,6 +341,8 @@ namespace experimental::execution
 
       struct scheduler
       {
+        using scheduler_concept = scheduler_tag;
+
        private:
         template <class Receiver>
         friend struct _opstate;
diff --git a/include/exec/thread_pool_base.hpp b/include/exec/thread_pool_base.hpp
index 47a892204..09c278d46 100644
--- a/include/exec/thread_pool_base.hpp
+++ b/include/exec/thread_pool_base.hpp
@@ -138,6 +138,8 @@ namespace experimental::execution
 
     struct scheduler
     {
+      using scheduler_concept = STDEXEC::scheduler_tag;
+
      private:
       template <class DerivedPoolType_, class Receiver>
       friend struct _pool_::opstate;
diff --git a/include/exec/timed_thread_scheduler.hpp b/include/exec/timed_thread_scheduler.hpp
index b84f1d8f4..45a8914d8 100644
--- a/include/exec/timed_thread_scheduler.hpp
+++ b/include/exec/timed_thread_scheduler.hpp
@@ -365,8 +365,9 @@ namespace experimental::execution
   class timed_thread_scheduler
   {
    public:
-    using time_point = std::chrono::steady_clock::time_point;
-    using duration   = std::chrono::steady_clock::duration;
+    using scheduler_concept = STDEXEC::scheduler_tag;
+    using time_point        = std::chrono::steady_clock::time_point;
+    using duration          = std::chrono::steady_clock::duration;
 
     class schedule_at_sender
     {
diff --git a/include/exec/trampoline_scheduler.hpp b/include/exec/trampoline_scheduler.hpp
index c11a8eb63..449385ab1 100644
--- a/include/exec/trampoline_scheduler.hpp
+++ b/include/exec/trampoline_scheduler.hpp
@@ -111,6 +111,8 @@ namespace experimental::execution
       std::size_t __max_recursion_size_;
 
      public:
+      using scheduler_concept = scheduler_tag;
+
       constexpr __scheduler() noexcept
         : __attrs{16}
         , __max_recursion_size_(4096)
diff --git a/include/exec/windows/windows_thread_pool.hpp b/include/exec/windows/windows_thread_pool.hpp
index 0ca885c68..f41776d52 100644
--- a/include/exec/windows/windows_thread_pool.hpp
+++ b/include/exec/windows/windows_thread_pool.hpp
@@ -891,7 +891,8 @@ namespace experimental::execution::__win32
   class windows_thread_pool::scheduler
   {
    public:
-    using time_point = filetime_clock::time_point;
+    using scheduler_concept = STDEXEC::scheduler_tag;
+    using time_point        = filetime_clock::time_point;
 
     [[nodiscard]]
     auto schedule() const noexcept -> schedule_sender
diff --git a/include/nvexec/multi_gpu_context.cuh b/include/nvexec/multi_gpu_context.cuh
index 77a452245..3f5940693 100644
--- a/include/nvexec/multi_gpu_context.cuh
+++ b/include/nvexec/multi_gpu_context.cuh
@@ -31,6 +31,8 @@ namespace nv::execution
   {
     struct multi_gpu_stream_scheduler : private stream_scheduler_env<multi_gpu_stream_scheduler>
     {
+      using scheduler_concept = STDEXEC::scheduler_tag;
+
       multi_gpu_stream_scheduler(int num_devices, context ctx)
         : num_devices_(num_devices)
         , ctx_(ctx)
diff --git a/include/nvexec/stream_context.cuh b/include/nvexec/stream_context.cuh
index 5d5b60342..deb5fc4ef 100644
--- a/include/nvexec/stream_context.cuh
+++ b/include/nvexec/stream_context.cuh
@@ -69,6 +69,8 @@ namespace nv::execution
 
     struct stream_scheduler : private stream_scheduler_env<stream_scheduler>
     {
+      using scheduler_concept = STDEXEC::scheduler_tag;
+
       explicit stream_scheduler(context ctx) noexcept
         : ctx_(ctx)
       {}
diff --git a/include/stdexec/__detail/__parallel_scheduler.hpp b/include/stdexec/__detail/__parallel_scheduler.hpp
index 954e9d074..821e439f7 100644
--- a/include/stdexec/__detail/__parallel_scheduler.hpp
+++ b/include/stdexec/__detail/__parallel_scheduler.hpp
@@ -293,6 +293,8 @@ namespace STDEXEC
   class parallel_scheduler
   {
    public:
+    using scheduler_concept = scheduler_tag;
+
     parallel_scheduler() = delete;
 
     /// Returns `true` iff `*this` refers to the same scheduler as the argument.
diff --git a/test/exec/test_task.cpp b/test/exec/test_task.cpp
index dfc1e2d0e..97f036f59 100644
--- a/test/exec/test_task.cpp
+++ b/test/exec/test_task.cpp
@@ -21,7 +21,9 @@
 #  include <exec/async_scope.hpp>
 #  include <exec/sender_for.hpp>
 #  include <exec/single_thread_context.hpp>
+#  include <exec/static_thread_pool.hpp>
 #  include <exec/task.hpp>
+#  include <exec/timed_thread_scheduler.hpp>
 
 #  include <test_common/schedulers.hpp>
 
@@ -370,6 +372,42 @@ namespace
     CHECK(count == 3);
   }
 #  endif  // !STDEXEC_NO_STDCPP_EXCEPTIONS()
+
+  // Regression tests for https://github.com/NVIDIA/stdexec/issues/2134: the
+  // schedulers of exec::static_thread_pool and exec::timed_thread_context used
+  // to be missing the `scheduler_concept` nested alias required by the
+  // scheduler concept, which made exec::task's internal __any_scheduler
+  // conversion fail to compile when such a task was co_started on them.
+  TEST_CASE("task - can be started on a static_thread_pool scheduler", "[types][task]")
+  {
+    exec::static_thread_pool pool{2};
+    bool                     ran = false;
+    // Keep the closure a temporary inside the full expression: the task is
+    // lazy, so the closure (and its by-reference capture) must outlive the
+    // point at which the pool thread resumes the coroutine.
+    auto op_state = STDEXEC::sync_wait(STDEXEC::starts_on(pool.get_scheduler(),
+                                                          [&]() -> exec::task<void>
+                                                          {
+                                                            ran = true;
+                                                            co_return;
+                                                          }()));
+    REQUIRE(op_state);
+    CHECK(ran);
+  }
+
+  TEST_CASE("task - can be started on a timed_thread_context scheduler", "[types][task]")
+  {
+    exec::timed_thread_context ctx;
+    bool                       ran      = false;
+    auto                       op_state = STDEXEC::sync_wait(STDEXEC::starts_on(ctx.get_scheduler(),
+                                                          [&]() -> exec::task<void>
+                                                          {
+                                                            ran = true;
+                                                            co_return;
+                                                          }()));
+    REQUIRE(op_state);
+    CHECK(ran);
+  }
 }  // namespace
 
 #endif