Index: ELF/InputFiles.cpp
===================================================================
--- ELF/InputFiles.cpp
+++ ELF/InputFiles.cpp
@@ -537,7 +537,8 @@
     return &InputSection::Discarded;
   }
 
-  if (Config->Strip != StripPolicy::None && Name.startswith(".debug"))
+  if (Config->Strip != StripPolicy::None &&
+      (Name.startswith(".debug") || Name.startswith(".zdebug")))
     return &InputSection::Discarded;
 
   // The linkonce feature is a sort of proto-comdat. Some glibc i386 object
Index: test/ELF/strip-debug.s
===================================================================
--- test/ELF/strip-debug.s
+++ test/ELF/strip-debug.s
@@ -1,25 +1,14 @@
 # REQUIRES: x86
-
-# RUN: llvm-mc -filetype=obj -triple=x86_64-unknown-linux -g %s -o %t
-# RUN: ld.lld %t -o %t2
-# RUN: llvm-readobj -sections -symbols %t2 | FileCheck -check-prefix=DEFAULT %s
+# RUN: llvm-mc -filetype=obj -triple=x86_64-unknown-linux %s -o %t
 # RUN: ld.lld %t -o %t2 --strip-debug
-# RUN: llvm-readobj -sections -symbols %t2 | FileCheck -check-prefix=STRIP %s
+# RUN: llvm-readobj -sections %t2 | FileCheck %s
 # RUN: ld.lld %t -o %t2 -S
-# RUN: llvm-readobj -sections -symbols %t2 | FileCheck -check-prefix=STRIP %s
+# RUN: llvm-readobj -sections %t2 | FileCheck %s
 # RUN: ld.lld %t -o %t2 --strip-all
-# RUN: llvm-readobj -sections -symbols %t2 | FileCheck -check-prefix=STRIP %s
-
-# DEFAULT: Name: .debug_info
-# DEFAULT: Name: .debug_abbrev
-# DEFAULT: Name: .debug_aranges
-# DEFAULT: Name: .debug_line
+# RUN: llvm-readobj -sections %t2 | FileCheck %s
 
-# STRIP-NOT: Name: .debug_info
-# STRIP-NOT: Name: .debug_abbrev
-# STRIP-NOT: Name: .debug_aranges
-# STRIP-NOT: Name: .debug_line
+# CHECK-NOT: Foo
+# CHECK-NOT: Bar
 
-.globl _start
-_start:
-  ret
+.section .debug_Foo,"",@progbits
+.section .zdebug_Bar,"",@progbits