diff --git a/Source/cmTargetLinkLibrariesCommand.cxx b/Source/cmTargetLinkLibrariesCommand.cxx
index 22f6a0361..0707c626d 100644
--- a/Source/cmTargetLinkLibrariesCommand.cxx
+++ b/Source/cmTargetLinkLibrariesCommand.cxx
@@ -151,7 +151,8 @@ bool cmTargetLinkLibrariesCommand
     else if(args[i] == "LINK_PUBLIC")
       {
       if(i != 1
-          && this->CurrentProcessingState != ProcessingPlainPrivateInterface)
+          && this->CurrentProcessingState != ProcessingPlainPrivateInterface
+          && this->CurrentProcessingState != ProcessingPlainPublicInterface)
         {
         this->Makefile->IssueMessage(
           cmake::FATAL_ERROR,
@@ -181,7 +182,8 @@ bool cmTargetLinkLibrariesCommand
     else if(args[i] == "LINK_PRIVATE")
       {
       if(i != 1
-          && this->CurrentProcessingState != ProcessingPlainPublicInterface)
+          && this->CurrentProcessingState != ProcessingPlainPublicInterface
+          && this->CurrentProcessingState != ProcessingPlainPrivateInterface)
         {
         this->Makefile->IssueMessage(
           cmake::FATAL_ERROR,
diff --git a/Tests/CMakeCommands/target_link_libraries/CMakeLists.txt b/Tests/CMakeCommands/target_link_libraries/CMakeLists.txt
index 06019e691..e11f980df 100644
--- a/Tests/CMakeCommands/target_link_libraries/CMakeLists.txt
+++ b/Tests/CMakeCommands/target_link_libraries/CMakeLists.txt
@@ -32,7 +32,7 @@ generate_export_header(depA)
 add_library(depB SHARED depB.cpp)
 generate_export_header(depB)
 
-target_link_libraries(depB LINK_PRIVATE depA)
+target_link_libraries(depB LINK_PRIVATE depA LINK_PRIVATE depA)
 
 add_library(libgenex SHARED libgenex.cpp)
 generate_export_header(libgenex)
@@ -44,11 +44,11 @@ set_property(TARGET depB APPEND PROPERTY
 add_library(depC SHARED depC.cpp)
 generate_export_header(depC)
 
-target_link_libraries(depC LINK_PUBLIC depA)
+target_link_libraries(depC LINK_PUBLIC depA LINK_PUBLIC depA)
 
 assert_property(depA LINK_INTERFACE_LIBRARIES "")
 assert_property(depB LINK_INTERFACE_LIBRARIES "")
-assert_property(depC LINK_INTERFACE_LIBRARIES "depA")
+assert_property(depC LINK_INTERFACE_LIBRARIES "depA;depA")
 
 add_executable(targetA targetA.cpp)