Index: /trunk/src/org/openstreetmap/josm/gui/layer/AutosaveTask.java
===================================================================
--- /trunk/src/org/openstreetmap/josm/gui/layer/AutosaveTask.java	(revision 17180)
+++ /trunk/src/org/openstreetmap/josm/gui/layer/AutosaveTask.java	(revision 17181)
@@ -17,4 +17,5 @@
 import java.util.Arrays;
 import java.util.Collections;
+import java.util.Comparator;
 import java.util.Date;
 import java.util.Deque;
@@ -150,5 +151,9 @@
             File[] files = deletedLayersDir.listFiles();
             if (files != null) {
-                // FIXME: sort by mtime
+                try {
+                    Arrays.sort(files, Comparator.comparingLong(File::lastModified));
+                } catch (Exception e) {
+                    Logging.error(e);
+                }
                 deletedLayers.addAll(Arrays.asList(files));
             }