diff --git a/Source/cmExportFileGenerator.cxx b/Source/cmExportFileGenerator.cxx
index e8a2e6a52..c005995f7 100644
--- a/Source/cmExportFileGenerator.cxx
+++ b/Source/cmExportFileGenerator.cxx
@@ -772,6 +772,27 @@ cmExportFileGenerator::ResolveTargetsInGeneratorExpression(
     lastPos = endPos;
     }
 
+  pos = 0;
+  lastPos = pos;
+  while (errorString.empty() &&
+         (pos = input.find("$<LINK_ONLY:", lastPos)) != input.npos)
+    {
+    std::string::size_type nameStartPos = pos + sizeof("$<LINK_ONLY:") - 1;
+    std::string::size_type endPos = input.find(">", nameStartPos);
+    if (endPos == input.npos)
+      {
+      errorString = "$<LINK_ONLY:...> expression incomplete";
+      break;
+      }
+    std::string libName = input.substr(nameStartPos, endPos - nameStartPos);
+    if (cmGeneratorExpression::IsValidTargetName(libName) &&
+        this->AddTargetNamespace(libName, target, missingTargets))
+      {
+      input.replace(nameStartPos, endPos - nameStartPos, libName);
+      }
+    lastPos = nameStartPos + libName.size() + 1;
+    }
+
   this->ReplaceInstallPrefix(input);
 
   if (!errorString.empty())
diff --git a/Source/cmTargetLinkLibrariesCommand.cxx b/Source/cmTargetLinkLibrariesCommand.cxx
index 5f3246ace..435346a30 100644
--- a/Source/cmTargetLinkLibrariesCommand.cxx
+++ b/Source/cmTargetLinkLibrariesCommand.cxx
@@ -432,11 +432,8 @@ cmTargetLinkLibrariesCommand::HandleLibrary(const std::string& lib,
         {
         std::string configLib = this->Target
                                      ->GetDebugGeneratorExpressions(lib, llt);
-        if (cmGeneratorExpression::IsValidTargetName(configLib))
-          {
-          configLib = "$<LINK_ONLY:$<TARGET_NAME:" + configLib + ">>";
-          }
-        else if (cmGeneratorExpression::Find(configLib) != std::string::npos)
+        if (cmGeneratorExpression::IsValidTargetName(lib)
+            || cmGeneratorExpression::Find(lib) != std::string::npos)
           {
           configLib = "$<LINK_ONLY:" + configLib + ">";
           }
diff --git a/Tests/RunCMake/target_link_libraries/RunCMakeTest.cmake b/Tests/RunCMake/target_link_libraries/RunCMakeTest.cmake
index 8307607bc..1466fbf61 100644
--- a/Tests/RunCMake/target_link_libraries/RunCMakeTest.cmake
+++ b/Tests/RunCMake/target_link_libraries/RunCMakeTest.cmake
@@ -8,3 +8,5 @@ run_cmake(MixedSignature)
 run_cmake(Separate-PRIVATE-LINK_PRIVATE-uses)
 run_cmake(SubDirTarget)
 run_cmake(SharedDepNotTarget)
+run_cmake(StaticPrivateDepNotExported)
+run_cmake(StaticPrivateDepNotTarget)
diff --git a/Tests/RunCMake/target_link_libraries/StaticPrivateDepNotExported-result.txt b/Tests/RunCMake/target_link_libraries/StaticPrivateDepNotExported-result.txt
new file mode 100644
index 000000000..d00491fd7
--- /dev/null
+++ b/Tests/RunCMake/target_link_libraries/StaticPrivateDepNotExported-result.txt
@@ -0,0 +1 @@
+1
diff --git a/Tests/RunCMake/target_link_libraries/StaticPrivateDepNotExported-stderr.txt b/Tests/RunCMake/target_link_libraries/StaticPrivateDepNotExported-stderr.txt
new file mode 100644
index 000000000..6bb44ab4b
--- /dev/null
+++ b/Tests/RunCMake/target_link_libraries/StaticPrivateDepNotExported-stderr.txt
@@ -0,0 +1 @@
+CMake Error: install\(EXPORT "Exp" ...\) includes target "foo" which requires target "not_exported" that is not in the export set.
diff --git a/Tests/RunCMake/target_link_libraries/StaticPrivateDepNotExported.cmake b/Tests/RunCMake/target_link_libraries/StaticPrivateDepNotExported.cmake
new file mode 100644
index 000000000..9b97918a5
--- /dev/null
+++ b/Tests/RunCMake/target_link_libraries/StaticPrivateDepNotExported.cmake
@@ -0,0 +1,7 @@
+cmake_policy(SET CMP0022 NEW)
+enable_language(C)
+add_library(foo STATIC empty.c)
+add_library(not_exported STATIC empty.c)
+target_link_libraries(foo PRIVATE not_exported)
+install(TARGETS foo EXPORT Exp DESTINATION lib)
+install(EXPORT Exp DESTINATION lib/cmake/Exp)
diff --git a/Tests/RunCMake/target_link_libraries/StaticPrivateDepNotTarget.cmake b/Tests/RunCMake/target_link_libraries/StaticPrivateDepNotTarget.cmake
new file mode 100644
index 000000000..7122ae91e
--- /dev/null
+++ b/Tests/RunCMake/target_link_libraries/StaticPrivateDepNotTarget.cmake
@@ -0,0 +1,6 @@
+cmake_policy(SET CMP0022 NEW)
+enable_language(C)
+add_library(foo STATIC empty.c)
+target_link_libraries(foo PRIVATE not_a_target)
+install(TARGETS foo EXPORT Exp DESTINATION lib)
+install(EXPORT Exp DESTINATION lib/cmake/Exp)