Index: test/tools/llvm-objcopy/ELF/Inputs/compress-debug-sections.yaml
===================================================================
--- test/tools/llvm-objcopy/ELF/Inputs/compress-debug-sections.yaml
+++ test/tools/llvm-objcopy/ELF/Inputs/compress-debug-sections.yaml
@@ -25,6 +25,23 @@
   - Name:            .debug_bar
     Type:            SHT_PROGBITS
     Content:         0000000000000000
+  - Name:            .group
+    Type:            SHT_GROUP
+    Link:            .symtab
+    EntSize:         0x0000000000000004
+    Info:            groupname
+    Members:         
+      - SectionOrType:   GRP_COMDAT
+      - SectionOrType:   .text.in.group
+      - SectionOrType:   .debug_in_group
+  - Name:            .text.in.group
+    Type:            SHT_PROGBITS
+    Flags:           [ SHF_ALLOC, SHF_EXECINSTR, SHF_GROUP ]
+    Content:         '00'
+  - Name:            .debug_in_group
+    Type:            SHT_PROGBITS
+    Flags:           [ SHF_GROUP ]
+    Content:         '00'
 Symbols:
   Global:
     - Name:    .debug_foo
@@ -35,4 +52,6 @@
       Section: .notdebug_foo
     - Name:    .Linfo_string0
       Section: .debug_bar
+    - Name:    groupname
+      Section: .group
 ...
Index: test/tools/llvm-objcopy/ELF/compress-debug-sections-groups.test
===================================================================
--- /dev/null
+++ test/tools/llvm-objcopy/ELF/compress-debug-sections-groups.test
@@ -0,0 +1,53 @@
+# REQUIRES: zlib
+
+## In this test, we check how tool handles compression/decompression
+## of debug section included in a COMDAT group.
+
+# RUN: yaml2obj %p/Inputs/compress-debug-sections.yaml -o %t.o
+
+## Check how we compress debug section.
+# RUN: llvm-objcopy --compress-debug-sections %t.o %t-compressed.o
+# RUN: llvm-readobj -s -elf-section-groups %t-compressed.o | \
+# RUN:   FileCheck %s --check-prefixes=CHECK,COMPRESS
+
+## Check how we compress debug section with zlib-gnu.
+# RUN: llvm-objcopy --compress-debug-sections=zlib-gnu %t.o %t-compressed-gnu.o
+# RUN: llvm-readobj -s -elf-section-groups %t-compressed-gnu.o | \
+# RUN:   FileCheck %s --check-prefixes=CHECK,COMPRESSZLIB
+
+## Check how we decompress debug section.
+# RUN: llvm-objcopy --decompress-debug-sections %t-compressed.o %t-decompressed.o
+# RUN: llvm-readobj -elf-section-groups %t-decompressed.o | \
+# RUN:   FileCheck %s --check-prefixes=CHECK,DECOMPRESS
+
+## Check how we decompress zlib-gnu debug section.
+# RUN: llvm-objcopy --decompress-debug-sections %t-compressed-gnu.o %t-decompressed-gnu.o
+# RUN: llvm-readobj -elf-section-groups %t-decompressed-gnu.o | \
+# RUN:   FileCheck %s --check-prefixes=CHECK,DECOMPRESS
+
+# COMPRESSZLIB:      Name: .zdebug_in_group
+# COMPRESSZLIB-NEXT: Type: SHT_PROGBITS
+# COMPRESSZLIB-NEXT: Flags [
+# COMPRESSZLIB-NEXT:   SHF_GROUP
+# COMPRESSZLIB-NEXT: ]
+
+# COMPRESS:      Name: .debug_in_group
+# COMPRESS-NEXT: Type: SHT_PROGBITS
+# COMPRESS-NEXT: Flags [
+# COMPRESS-NEXT:   SHF_COMPRESSED
+# COMPRESS-NEXT:   SHF_GROUP
+# COMPRESS-NEXT: ]
+
+# CHECK:           Group {
+# CHECK-NEXT:        Name: .group
+# CHECK-NEXT:        Index:
+# CHECK-NEXT:        Link:
+# CHECK-NEXT:        Info:
+# CHECK-NEXT:        Type: COMDAT
+# CHECK-NEXT:        Signature: groupname
+# CHECK-NEXT:        Section(s) in group [
+# CHECK-NEXT:          .text.in.group
+# COMPRESSZLIB-NEXT:   .zdebug_in_group
+# COMPRESS-NEXT:       .debug_in_group
+# DECOMPRESS-NEXT:     .debug_in_group
+# CHECK-NEXT:        ]
Index: tools/llvm-objcopy/ELF/Object.h
===================================================================
--- tools/llvm-objcopy/ELF/Object.h
+++ tools/llvm-objcopy/ELF/Object.h
@@ -633,6 +633,8 @@
   void finalize() override;
   Error removeSymbols(function_ref<bool(const Symbol &)> ToRemove) override;
   void markSymbols() override;
+  void replaceSectionReferences(
+      const DenseMap<SectionBase *, SectionBase *> &FromTo) override;
 
   static bool classof(const SectionBase *S) {
     return S->Type == ELF::SHT_GROUP;
Index: tools/llvm-objcopy/ELF/Object.cpp
===================================================================
--- tools/llvm-objcopy/ELF/Object.cpp
+++ tools/llvm-objcopy/ELF/Object.cpp
@@ -689,6 +689,13 @@
     Sym->Referenced = true;
 }
 
+void GroupSection::replaceSectionReferences(
+    const DenseMap<SectionBase *, SectionBase *> &FromTo) {
+  for (SectionBase *&Sec : GroupMembers)
+    if (SectionBase *To = FromTo.lookup(Sec))
+      Sec = To;
+}
+
 void Section::initialize(SectionTableRef SecTable) {
   if (Link != ELF::SHN_UNDEF) {
     LinkSection =