diff --git a/llvm/docs/LangRef.rst b/llvm/docs/LangRef.rst
--- a/llvm/docs/LangRef.rst
+++ b/llvm/docs/LangRef.rst
@@ -894,6 +894,11 @@
 * No global value in the expression can be a declaration, since that
   would require a relocation, which is not possible.
 
+* If either the alias or the aliasee may be replaced by a symbol outside the
+  module at link time or runtime, any optimization cannot replace the alias with
+  the aliasee, since the behavior may be different. The alias may be used as a
+  name guaranteed to point to the content in the current module.
+
 .. _langref_ifunc:
 
 IFuncs
diff --git a/llvm/lib/Transforms/IPO/GlobalOpt.cpp b/llvm/lib/Transforms/IPO/GlobalOpt.cpp
--- a/llvm/lib/Transforms/IPO/GlobalOpt.cpp
+++ b/llvm/lib/Transforms/IPO/GlobalOpt.cpp
@@ -2253,6 +2253,13 @@
   for (GlobalValue *GV : Used.used())
     Used.compilerUsedErase(GV);
 
+  // Return whether GV is explicitly or implicitly dso_local and not replaceable
+  // by another definition in the current linkage unit.
+  auto IsModuleLocal = [](GlobalValue &GV) {
+    return !GlobalValue::isInterposableLinkage(GV.getLinkage()) &&
+           (GV.isDSOLocal() || GV.isImplicitDSOLocal());
+  };
+
   for (GlobalAlias &J : llvm::make_early_inc_range(M.aliases())) {
     // Aliases without names cannot be referenced outside this module.
     if (!J.hasName() && !J.isDeclaration() && !J.hasLocalLinkage())
@@ -2264,18 +2271,20 @@
     }
 
     // If the alias can change at link time, nothing can be done - bail out.
-    if (J.isInterposable())
+    if (!IsModuleLocal(J))
       continue;
 
     Constant *Aliasee = J.getAliasee();
     GlobalValue *Target = dyn_cast<GlobalValue>(Aliasee->stripPointerCasts());
     // We can't trivially replace the alias with the aliasee if the aliasee is
     // non-trivial in some way. We also can't replace the alias with the aliasee
-    // if the aliasee is interposable because aliases point to the local
-    // definition.
+    // if the aliasee may be preemptible at runtime. On ELF, a non-preemptible
+    // alias can be used to access the definition as if preemption did not
+    // happen.
     // TODO: Try to handle non-zero GEPs of local aliasees.
-    if (!Target || Target->isInterposable())
+    if (!Target || !IsModuleLocal(*Target))
       continue;
+
     Target->removeDeadConstantUsers();
 
     // Make all users of the alias use the aliasee instead.
diff --git a/llvm/test/Transforms/GlobalOpt/2009-02-15-ResolveAlias.ll b/llvm/test/Transforms/GlobalOpt/2009-02-15-ResolveAlias.ll
--- a/llvm/test/Transforms/GlobalOpt/2009-02-15-ResolveAlias.ll
+++ b/llvm/test/Transforms/GlobalOpt/2009-02-15-ResolveAlias.ll
@@ -2,13 +2,13 @@
 
 define internal void @f() {
 ; CHECK-NOT: @f(
-; CHECK: define void @a
+; CHECK: define dso_local void @a
 	ret void
 }
 
-@a = alias void (), void ()* @f
+@a = dso_local alias void (), void ()* @f
 
-define void @g() {
+define hidden void @g() {
 	call void() @a()
 	ret void
 }
diff --git a/llvm/test/Transforms/GlobalOpt/alias-resolve.ll b/llvm/test/Transforms/GlobalOpt/alias-resolve.ll
--- a/llvm/test/Transforms/GlobalOpt/alias-resolve.ll
+++ b/llvm/test/Transforms/GlobalOpt/alias-resolve.ll
@@ -1,16 +1,19 @@
 ; RUN: opt < %s -passes=globalopt -S | FileCheck %s
 
 @foo1 = alias void (), void ()* @foo2
+;; foo2 is dso_local and non-weak. Resolved.
 ; CHECK: @foo1 = alias void (), void ()* @bar2
 
-@foo2 = alias void(), void()* @bar1
-; CHECK: @foo2 = alias void (), void ()* @bar2
+@foo2 = dso_local alias void(), void()* @bar1
+;; bar1 is dso_local and non-weak. Resolved.
+; CHECK: @foo2 = dso_local alias void (), void ()* @bar2
 
-@bar1  = alias void (), void ()* @bar2
-; CHECK: @bar1 = alias void (), void ()* @bar2
+@bar1  = dso_local alias void (), void ()* @bar2
+; CHECK: @bar1 = dso_local alias void (), void ()* @bar2
 
-@weak1 = weak alias void (), void ()* @bar2
-; CHECK: @weak1 = weak alias void (), void ()* @bar2
+@weak1 = weak dso_local alias void (), void ()* @bar2
+;; weak1 may be replaced with another definition in the linkage unit. Not resolved.
+; CHECK: @weak1 = weak dso_local alias void (), void ()* @bar2
 
 @bar4 = private unnamed_addr constant [2 x i8*] zeroinitializer
 @foo4 = weak_odr unnamed_addr alias i8*, getelementptr inbounds ([2 x i8*], [2 x i8*]* @bar4, i32 0, i32 1)
@@ -19,10 +22,10 @@
 @priva  = private alias void (), void ()* @bar5
 ; CHECK: @priva = private alias void (), void ()* @bar5
 
-define void @bar2() {
+define dso_local void @bar2() {
   ret void
 }
-; CHECK: define void @bar2()
+; CHECK: define dso_local void @bar2()
 
 define weak void @bar5() {
   ret void
@@ -32,27 +35,32 @@
 define void @baz() {
 entry:
          call void @foo1()
-; CHECK: call void @bar2()
+;; foo1 is dso_preemptable. Not resolved.
+; CHECK: call void @foo1()
 
          call void @foo2()
+;; foo2 is dso_local and non-weak. Resolved.
 ; CHECK: call void @bar2()
 
          call void @bar1()
+;; bar1 is dso_local and non-weak. Resolved.
 ; CHECK: call void @bar2()
 
          call void @weak1()
+;; weak1 is weak. Not resolved.
 ; CHECK: call void @weak1()
 
          call void @priva()
+;; priva has a local linkage. Resolved.
 ; CHECK: call void @priva()
 
          ret void
 }
 
-@foo3 = alias void (), void ()* @bar3
+@foo3 = dso_local alias void (), void ()* @bar3
 ; CHECK-NOT: bar3
 
 define internal void @bar3() {
   ret void
 }
-;CHECK: define void @foo3
+;CHECK: define dso_local void @foo3
diff --git a/llvm/test/Transforms/GlobalOpt/alias-used-address-space.ll b/llvm/test/Transforms/GlobalOpt/alias-used-address-space.ll
--- a/llvm/test/Transforms/GlobalOpt/alias-used-address-space.ll
+++ b/llvm/test/Transforms/GlobalOpt/alias-used-address-space.ll
@@ -2,7 +2,7 @@
 
 target datalayout = "p:32:32:32-p1:16:16:16"
 
-@c = addrspace(1) global i8 42
+@c = hidden addrspace(1) global i8 42
 
 @i = internal addrspace(1) global i8 42
 
diff --git a/llvm/test/Transforms/GlobalOpt/alias-used.ll b/llvm/test/Transforms/GlobalOpt/alias-used.ll
--- a/llvm/test/Transforms/GlobalOpt/alias-used.ll
+++ b/llvm/test/Transforms/GlobalOpt/alias-used.ll
@@ -1,6 +1,6 @@
 ; RUN: opt < %s -passes=globalopt -S | FileCheck %s
 
-@c = global i8 42
+@c = dso_local global i8 42
 
 @i = internal global i8 42
 ; CHECK: @ia = internal global i8 42
@@ -30,7 +30,7 @@
 @ca = internal alias i8, i8* @c
 ; CHECK: @ca = internal alias i8, i8* @c
 
-define void @f() {
+define hidden void @f() {
   ret void
 }