diff --git a/lld/test/ELF/linkerscript/tls-nobits-offset.s b/lld/test/ELF/linkerscript/tls-nobits-offset.s
new file mode 100644
--- /dev/null
+++ b/lld/test/ELF/linkerscript/tls-nobits-offset.s
@@ -0,0 +1,31 @@
+# REQUIRES: x86
+# RUN: llvm-mc -filetype=obj -triple=x86_64-pc-linux %s -o %t.o
+# RUN: echo "SECTIONS { \
+# RUN:         .sec1          : { . += 1; } \
+# RUN:         .tbss          : { *(.tbss) } \
+# RUN:       };" > %t.script
+# RUN: ld.lld %t.o -T %t.script -o %t
+# RUN: llvm-readelf -S -l %t | FileCheck %s
+
+## If a SHT_NOBITS section is the only section of a PT_TLS segment,
+## p_offset will be set to the sh_offset field of the section. Check we align
+## sh_offset to sh_addr modulo p_align, so that p_vaddr=p_offset (mod
+## p_align).
+## TODO: Currently we fail to ensure this, as shown by this test
+
+# CHECK:      Name  Type     Address          Off     Size
+# CHECK-NEXT:       NULL     0000000000000000 000000  000000
+# CHECK-NEXT: .text PROGBITS 0000000000000000 000190  000000
+# CHECK-NEXT: .sec1 PROGBITS 0000000000000000 001000  000001
+# CHECK-NEXT: .tbss NOBITS   0000000000000400 001001  000001
+
+# CHECK:      Type Offset   VirtAddr           PhysAddr           FileSiz  MemSiz   Flg Align
+# CHECK-NEXT: LOAD 0x001000 0x0000000000000000 0x0000000000000000 0x000001 0x000001 R   0x1000
+# CHECK-NEXT: TLS  0x001001 0x0000000000000400 0x0000000000000400 0x000000 0x000001 R   0x400
+
+# CHECK:      00 .sec1 {{$}}
+# CHECK:      01 .tbss {{$}}
+
+.tbss
+.p2align 10
+.byte 0
diff --git a/lld/test/ELF/tls-nobits-offset.s b/lld/test/ELF/tls-nobits-offset.s
new file mode 100644
--- /dev/null
+++ b/lld/test/ELF/tls-nobits-offset.s
@@ -0,0 +1,22 @@
+# REQUIRES: aarch64
+# RUN: llvm-mc -filetype=obj -triple=aarch64 %s -o %t.o
+# RUN: ld.lld %t.o -o %t
+# RUN: llvm-readelf -S -l %t | FileCheck %s
+
+## If a SHT_NOBITS section is the only section of a PT_TLS segment,
+## p_offset will be set to the sh_offset field of the section. Check we align
+## sh_offset to sh_addr modulo p_align, so that p_vaddr=p_offset (mod
+## p_align).
+## TODO: Currently we fail to ensure this, as shown by this test
+
+# CHECK: Name  Type   Address          Off     Size   ES Flg Lk Inf Al
+# CHECK: .tbss NOBITS 0000000000211000 000158  000001 00 WAT  0   0 4096
+
+# CHECK: Type Offset   VirtAddr           PhysAddr           FileSiz  MemSiz   Flg Align
+# CHECK: TLS  0x000158 0x0000000000211000 0x0000000000211000 0x000000 0x000001 R   0x1000
+
+# CHECK: 02 .tbss
+
+.tbss
+.p2align 12
+.byte 0