Index: ELF/Writer.cpp
===================================================================
--- ELF/Writer.cpp
+++ ELF/Writer.cpp
@@ -1866,7 +1866,7 @@
   // Create one PT_NOTE per a group of contiguous .note sections.
   PhdrEntry *Note = nullptr;
   for (OutputSection *Sec : OutputSections) {
-    if (Sec->Type == SHT_NOTE) {
+    if (Sec->Type == SHT_NOTE && (Sec->Flags & SHF_ALLOC)) {
       if (!Note || Sec->LMAExpr)
         Note = AddHdr(PT_NOTE, PF_R);
       Note->add(Sec);
Index: test/ELF/note-noalloc.s
===================================================================
--- /dev/null
+++ test/ELF/note-noalloc.s
@@ -0,0 +1,22 @@
+// REQUIRES: x86
+// RUN: llvm-mc -filetype=obj -triple=x86_64-unknown-freebsd %s -o %t.o
+// RUN: ld.lld %t.o -o %t -shared
+// RUN: llvm-readobj -program-headers -sections %t | FileCheck %s
+
+// PR37361: A note without SHF_ALLOC should not create a PT_NOTE program
+// header (but should have a SHT_NOTE section).
+
+// CHECK: Name: .note.tag
+// CHECK: Type: SHT_NOTE
+// CHECK: Name: .debug.ghc-link-info
+// CHECK: Type: SHT_NOTE
+// CHECK-NOT: Type: SHT_NOTE
+
+// CHECK: Type: PT_NOTE
+// CHECK-NOT: Type: PT_NOTE
+
+        .section        .note.tag,"a",@note
+        .quad 1234
+
+        .section        .debug.ghc-link-info,"",@note
+        .quad 5678