diff --git a/llvm/docs/LangRef.rst b/llvm/docs/LangRef.rst
--- a/llvm/docs/LangRef.rst
+++ b/llvm/docs/LangRef.rst
@@ -6224,7 +6224,9 @@
    * - 2
      - **Warning**
            Emits a warning if two values disagree. The result value will be the
-           operand for the flag from the first module being linked.
+           operand for the flag from the first module being linked, or the max
+           if the other module uses **Max** (in which case the resulting flag
+           will be **Max**).
 
    * - 3
      - **Require**
diff --git a/llvm/lib/Linker/IRMover.cpp b/llvm/lib/Linker/IRMover.cpp
--- a/llvm/lib/Linker/IRMover.cpp
+++ b/llvm/lib/Linker/IRMover.cpp
@@ -1277,11 +1277,17 @@
     }
 
     // Diagnose inconsistent merge behavior types.
-    if (SrcBehaviorValue != DstBehaviorValue)
-      return stringErr("linking module flags '" + ID->getString() +
-                       "': IDs have conflicting behaviors in '" +
-                       SrcM->getModuleIdentifier() + "' and '" +
-                       DstM.getModuleIdentifier() + "'");
+    if (SrcBehaviorValue != DstBehaviorValue) {
+      bool MaxAndWarn = (SrcBehaviorValue == Module::Max &&
+                         DstBehaviorValue == Module::Warning) ||
+                        (DstBehaviorValue == Module::Max &&
+                         SrcBehaviorValue == Module::Warning);
+      if (!MaxAndWarn)
+        return stringErr("linking module flags '" + ID->getString() +
+                         "': IDs have conflicting behaviors in '" +
+                         SrcM->getModuleIdentifier() + "' and '" +
+                         DstM.getModuleIdentifier() + "'");
+    }
 
     auto replaceDstValue = [&](MDNode *New) {
       Metadata *FlagOps[] = {DstOp->getOperand(0), ID, New};
@@ -1290,6 +1296,20 @@
       Flags[ID].first = Flag;
     };
 
+    // Emit a warning if the values differ.
+    if ((DstBehaviorValue == Module::Warning ||
+         SrcBehaviorValue == Module::Warning) &&
+        SrcOp->getOperand(2) != DstOp->getOperand(2)) {
+      std::string Str;
+      raw_string_ostream(Str)
+          << "linking module flags '" << ID->getString()
+          << "': IDs have conflicting values ('" << *SrcOp->getOperand(2)
+          << "' from " << SrcM->getModuleIdentifier() << " with '"
+          << *DstOp->getOperand(2) << "' from " << DstM.getModuleIdentifier()
+          << ')';
+      emitWarning(Str);
+    }
+
     // Perform the merge for standard behavior types.
     switch (SrcBehaviorValue) {
     case Module::Require:
@@ -1305,26 +1325,9 @@
       continue;
     }
     case Module::Warning: {
-      // Emit a warning if the values differ.
-      if (SrcOp->getOperand(2) != DstOp->getOperand(2)) {
-        std::string str;
-        raw_string_ostream(str)
-            << "linking module flags '" << ID->getString()
-            << "': IDs have conflicting values ('" << *SrcOp->getOperand(2)
-            << "' from " << SrcM->getModuleIdentifier() << " with '"
-            << *DstOp->getOperand(2) << "' from " << DstM.getModuleIdentifier()
-            << ')';
-        emitWarning(str);
-      }
-      continue;
+      break;
     }
     case Module::Max: {
-      ConstantInt *DstValue =
-          mdconst::extract<ConstantInt>(DstOp->getOperand(2));
-      ConstantInt *SrcValue =
-          mdconst::extract<ConstantInt>(SrcOp->getOperand(2));
-      if (SrcValue->getZExtValue() > DstValue->getZExtValue())
-        overrideDstValue();
       break;
     }
     case Module::Append: {
@@ -1350,6 +1353,20 @@
       break;
     }
     }
+
+    if (DstBehaviorValue == Module::Max || SrcBehaviorValue == Module::Max) {
+      ConstantInt *DstValue =
+          mdconst::extract<ConstantInt>(DstOp->getOperand(2));
+      ConstantInt *SrcValue =
+          mdconst::extract<ConstantInt>(SrcOp->getOperand(2));
+      Metadata *FlagOps[] = {
+          (DstBehaviorValue != Module::Max ? SrcOp : DstOp)->getOperand(0), ID,
+          (SrcValue->getZExtValue() > DstValue->getZExtValue() ? SrcOp : DstOp)
+              ->getOperand(2)};
+      MDNode *Flag = MDNode::get(DstM.getContext(), FlagOps);
+      DstModFlags->setOperand(DstIndex, Flag);
+      Flags[ID].first = Flag;
+    }
   }
 
   // Check all of the requirements.
diff --git a/llvm/test/Linker/Inputs/module-max-warn.ll b/llvm/test/Linker/Inputs/module-max-warn.ll
new file mode 100644
--- /dev/null
+++ b/llvm/test/Linker/Inputs/module-max-warn.ll
@@ -0,0 +1,3 @@
+!llvm.module.flags = !{!0, !1}
+!0 = !{i32 2, !"Combine Max and Warn", i32 4}
+!1 = !{i32 7, !"Combine Warn and Max", i32 5}
diff --git a/llvm/test/Linker/module-max-warn.ll b/llvm/test/Linker/module-max-warn.ll
new file mode 100644
--- /dev/null
+++ b/llvm/test/Linker/module-max-warn.ll
@@ -0,0 +1,12 @@
+; RUN: llvm-link %s %p/Inputs/module-max-warn.ll -S -o - 2>&1 | FileCheck %s
+
+; CHECK: warning: linking module flags 'Combine Max and Warn': IDs have conflicting values ('i32 4' from {{.*}}/test/Linker/Inputs/module-max-warn.ll with 'i32 2' from llvm-link)
+; CHECK: warning: linking module flags 'Combine Warn and Max': IDs have conflicting values ('i32 5' from {{.*}}/test/Linker/Inputs/module-max-warn.ll with 'i32 3' from llvm-link)
+
+
+; CHECK: !0 = !{i32 7, !"Combine Max and Warn", i32 4}
+; CHECK: !1 = !{i32 7, !"Combine Warn and Max", i32 5}
+
+!llvm.module.flags = !{!0, !1}
+!0 = !{i32 7, !"Combine Max and Warn", i32 2}
+!1 = !{i32 2, !"Combine Warn and Max", i32 3}