diff --git a/gdb/python/lib/gdb/dap/next.py b/gdb/python/lib/gdb/dap/next.py
index 232b1529fe5..290b9b855ba 100644
--- a/gdb/python/lib/gdb/dap/next.py
+++ b/gdb/python/lib/gdb/dap/next.py
@@ -13,21 +13,40 @@
 # You should have received a copy of the GNU General Public License
 # along with this program.  If not, see <http://www.gnu.org/licenses/>.
 
+import gdb
+
 from .events import StopKinds, ExecutionInvoker
 from .server import capability, request
-from .startup import send_gdb
+from .startup import in_gdb_thread, send_gdb, send_gdb_with_response
 from .state import set_thread
 
 
-# Helper function to set the current thread.
-def _handle_thread_step(threadId):
+# Helper function to set the current thread and the scheduler-locking
+# mode.  Returns True if scheduler-locking was successfully set to
+# 'on', False in all other cases, including error.
+@in_gdb_thread
+def _handle_thread_step(thread_id, single_thread):
     # Ensure we're going to step the correct thread.
-    send_gdb(lambda: set_thread(threadId))
+    set_thread(thread_id)
+    if single_thread:
+        result = True
+        arg = "on"
+    else:
+        result = False
+        arg = "off"
+    try:
+        # This can fail, depending on the target, so catch the error
+        # and report to our caller.  We can't use exec_and_log because
+        # that does not propagate exceptions.
+        gdb.execute("set scheduler-locking " + arg, from_tty=True, to_string=True)
+    except gdb.error:
+        result = False
+    return result
 
 
 @request("next")
-def next(*, threadId, granularity="statement", **args):
-    _handle_thread_step(threadId)
+def next(*, threadId, singleThread=False, granularity="statement", **args):
+    send_gdb(lambda: _handle_thread_step(threadId, singleThread))
     cmd = "next"
     if granularity == "instruction":
         cmd += "i"
@@ -35,9 +54,10 @@ def next(*, threadId, granularity="statement", **args):
 
 
 @capability("supportsSteppingGranularity")
+@capability("supportsSingleThreadExecutionRequests")
 @request("stepIn")
-def stepIn(*, threadId, granularity="statement", **args):
-    _handle_thread_step(threadId)
+def stepIn(*, threadId, singleThread=False, granularity="statement", **args):
+    send_gdb(lambda: _handle_thread_step(threadId, singleThread))
     cmd = "step"
     if granularity == "instruction":
         cmd += "i"
@@ -45,12 +65,13 @@ def stepIn(*, threadId, granularity="statement", **args):
 
 
 @request("stepOut")
-def step_out(*, threadId):
-    _handle_thread_step(threadId)
+def step_out(*, threadId, singleThread=False):
+    send_gdb(lambda: _handle_thread_step(threadId, singleThread))
     send_gdb(ExecutionInvoker("finish", StopKinds.STEP))
 
 
 @request("continue")
-def continue_request(**args):
+def continue_request(*, threadId, singleThread=False, **args):
+    locked = send_gdb_with_response(lambda: _handle_thread_step(threadId, singleThread))
     send_gdb(ExecutionInvoker("continue", None))
-    return {"allThreadsContinued": True}
+    return {"allThreadsContinued": not locked}
diff --git a/gdb/testsuite/gdb.dap/basic-dap.exp b/gdb/testsuite/gdb.dap/basic-dap.exp
index d4dbdac70ff..ce739875404 100644
--- a/gdb/testsuite/gdb.dap/basic-dap.exp
+++ b/gdb/testsuite/gdb.dap/basic-dap.exp
@@ -136,15 +136,18 @@ set obj [dap_check_request_and_response "evaluate global second time" \
 dap_match_values "global value after step" [lindex $obj 0] \
     "body result" 24
 
-dap_check_request_and_response "continue to address" continue
+dap_check_request_and_response "continue to address" continue \
+    {o threadId [i 1]}
 dap_wait_for_event_and_check "stopped at address breakpoint" stopped \
     "body reason" breakpoint \
     "body hitBreakpointIds" $insn_bpno
 
-dap_check_request_and_response "continue to line" continue
+dap_check_request_and_response "continue to line" continue \
+    {o threadId [i 1]}
 dap_wait_for_event_and_check "stopped at line breakpoint" stopped \
     "body reason" breakpoint \
-    "body hitBreakpointIds" $line_bpno
+    "body hitBreakpointIds" $line_bpno \
+    "body allThreadsStopped" true
 
 dap_check_request_and_response "return from function" stepOut \
     {o threadId [i 1]}
diff --git a/gdb/testsuite/gdb.dap/catch-exception.exp b/gdb/testsuite/gdb.dap/catch-exception.exp
index 6bfeb3ed87e..7f2e750b32e 100644
--- a/gdb/testsuite/gdb.dap/catch-exception.exp
+++ b/gdb/testsuite/gdb.dap/catch-exception.exp
@@ -57,7 +57,8 @@ dap_wait_for_event_and_check "stopped at first raise" stopped \
     "body reason" breakpoint \
     "body hitBreakpointIds" 2
 
-dap_check_request_and_response "continue to assert" continue
+dap_check_request_and_response "continue to assert" continue \
+    {o threadId [i 1]}
 dap_wait_for_event_and_check "stopped at assert" stopped \
     "body reason" breakpoint \
     "body hitBreakpointIds" 1
