diff --git a/llvm/lib/Transforms/Scalar/JumpThreading.cpp b/llvm/lib/Transforms/Scalar/JumpThreading.cpp
--- a/llvm/lib/Transforms/Scalar/JumpThreading.cpp
+++ b/llvm/lib/Transforms/Scalar/JumpThreading.cpp
@@ -2125,6 +2125,18 @@
   if (PredBB->getSinglePredecessor())
     return false;
 
+  // Don't thread through PredBB if it contains a successor edge to itself, in
+  // which case we would infinite loop.  Suppose we are threading an edge from
+  // PredPredBB through PredBB and BB to SuccBB with PredBB containing a
+  // successor edge to itself.  If we allowed jump threading in this case, we
+  // could duplicate PredBB and BB as, say, PredBB.thread and BB.thread.  Since
+  // PredBB.thread has a successor edge to PredBB, we would immediately come up
+  // with another jump threading opportunity from PredBB.thread through PredBB
+  // and BB to SuccBB.  This jump threading would repeatedly occur.  That is, we
+  // would keep peeling one iteration from PredBB.
+  if (llvm::find(successors(PredBB), PredBB) != succ_end(PredBB))
+    return false;
+
   // Don't thread across a loop header.
   if (LoopHeaders.count(PredBB))
     return false;
diff --git a/llvm/test/Transforms/JumpThreading/PR44611-across-header-hang.ll b/llvm/test/Transforms/JumpThreading/PR44611-across-header-hang.ll
new file mode 100644
--- /dev/null
+++ b/llvm/test/Transforms/JumpThreading/PR44611-across-header-hang.ll
@@ -0,0 +1,22 @@
+; RUN: opt -S < %s -jump-threading -jump-threading-across-loop-headers | FileCheck %s
+
+; CHECK-LABEL: @foo
+; Just check that we don't hang on this test.
+
+define void @foo(i32 %a) {
+bb_entry:
+  br label %bb_header
+
+bb_header:
+  %b = phi i32 [ %c, %bb_header ], [ 0, %bb_body1 ], [ 2, %bb_body2 ], [ 0, %bb_entry ]
+  %c = add nuw nsw i32 %b, 1
+  %d = icmp ult i32 %c, 6
+  br i1 %d, label %bb_header, label %bb_body1
+
+bb_body1:
+  %e = icmp eq i32 %a, 0
+  br i1 %e, label %bb_body2, label %bb_header
+
+bb_body2:
+  br label %bb_header
+}