diff --git a/glibc.changes b/glibc.changes
index 6cfd806..aadc590 100644
--- a/glibc.changes
+++ b/glibc.changes
@@ -1,3 +1,8 @@
+-------------------------------------------------------------------
+Tue Jan  7 10:28:36 UTC 2025 - Andreas Schwab <schwab@suse.de>
+
+- Correctly determine livepatching support
+
 -------------------------------------------------------------------
 Sun Jan  5 11:43:47 UTC 2025 - Andreas Schwab <schwab@suse.de>
 
diff --git a/glibc.spec b/glibc.spec
index 56578b9..d4fa25a 100644
--- a/glibc.spec
+++ b/glibc.spec
@@ -61,13 +61,6 @@
 %define with_gcc 13
 %endif
 
-# Enable support for livepatching.
-%ifarch x86_64
-%bcond_without livepatching
-%else
-%bcond_with livepatching
-%endif
-
 %bcond_with build_all
 %define build_main 1
 %define build_utils %{with build_all}
@@ -103,6 +96,24 @@ ExclusiveArch:  do_not_build
 %endif
 %define host_arch %{?cross_cpu}%{!?cross_cpu:%{_target_cpu}}
 
+# Enable support for livepatching.
+%define have_livepatching_support 0
+%if %{build_cross}
+%if "%{cross_arch}" == "x86_64"
+%define have_livepatching_support 1
+%endif
+%else
+%ifarch x86_64
+%define have_livepatching_support 1
+%endif
+%endif
+
+%if %{have_livepatching_support}
+%bcond_without livepatching
+%else
+%bcond_with livepatching
+%endif
+
 %if %{build_main}
 %define name_suffix %{nil}
 %else