diff --git a/openmp/libomptarget/test/libc/assert.c b/openmp/libomptarget/test/libc/assert.c
index 9a10032f48189..803a8207e10a4 100644
--- a/openmp/libomptarget/test/libc/assert.c
+++ b/openmp/libomptarget/test/libc/assert.c
@@ -3,6 +3,8 @@
 
 // REQUIRES: libc
 
+// NVPTX without LTO uses the implementation in OpenMP currently.
+// UNSUPPORTED: nvptx64-nvidia-cuda
 // UNSUPPORTED: powerpc64-ibm-linux-gnu
 // UNSUPPORTED: powerpc64-ibm-linux-gnu-LTO
 // UNSUPPORTED: aarch64-unknown-linux-gnu
diff --git a/openmp/libomptarget/test/mapping/target_derefence_array_pointrs.cpp b/openmp/libomptarget/test/mapping/target_derefence_array_pointrs.cpp
index 7d4bc9ea22478..a6dd4069a8f58 100644
--- a/openmp/libomptarget/test/mapping/target_derefence_array_pointrs.cpp
+++ b/openmp/libomptarget/test/mapping/target_derefence_array_pointrs.cpp
@@ -2,7 +2,10 @@
 // RUN: %libomptarget-run-generic 2>&1 \
 // RUN: | %fcheck-generic
 
+// FIXME: This is currently broken on all GPU targets
 // UNSUPPORTED: amdgcn-amd-amdhsa
+// UNSUPPORTED: nvptx64-nvidia-cuda
+// UNSUPPORTED: nvptx64-nvidia-cuda-LTO
 
 #include <stdio.h>
 #include <stdlib.h>
diff --git a/openmp/libomptarget/test/mapping/target_uses_allocator.c b/openmp/libomptarget/test/mapping/target_uses_allocator.c
index 87b940650b998..eb20e965c30bc 100755
--- a/openmp/libomptarget/test/mapping/target_uses_allocator.c
+++ b/openmp/libomptarget/test/mapping/target_uses_allocator.c
@@ -1,6 +1,9 @@
 // RUN: %libomptarget-compile-run-and-check-generic
 
+// FIXME: https://github.com/llvm/llvm-project/issues/77841
 // UNSUPPORTED: amdgcn-amd-amdhsa
+// UNSUPPORTED: nvptx64-nvidia-cuda
+// UNSUPPORTED: nvptx64-nvidia-cuda-LTO
 
 #include <omp.h>
 #include <stdio.h>
diff --git a/openmp/libomptarget/test/mapping/target_wrong_use_device_addr.c b/openmp/libomptarget/test/mapping/target_wrong_use_device_addr.c
index 6c7939ea196ad..7a5babd692530 100644
--- a/openmp/libomptarget/test/mapping/target_wrong_use_device_addr.c
+++ b/openmp/libomptarget/test/mapping/target_wrong_use_device_addr.c
@@ -2,6 +2,9 @@
 // RUN: env LIBOMPTARGET_INFO=64 %libomptarget-run-fail-generic 2>&1 \
 // RUN: | %fcheck-generic
 
+// FIXME: Fails due to optimized debugging in 'ptxas'
+// UNSUPPORTED: nvptx64-nvidia-cuda-LTO
+
 #include <stdio.h>
 
 int main() {
diff --git a/openmp/libomptarget/test/offloading/bug64959.c b/openmp/libomptarget/test/offloading/bug64959.c
index 500911fa3f316..eddc55325ffe9 100644
--- a/openmp/libomptarget/test/offloading/bug64959.c
+++ b/openmp/libomptarget/test/offloading/bug64959.c
@@ -1,8 +1,11 @@
-// RUN: %libomptarget-compilexx-run-and-check-generic
-// RUN: %libomptarget-compileoptxx-run-and-check-generic
+// RUN: %libomptarget-compile-run-and-check-generic
+// RUN: %libomptarget-compileopt-run-and-check-generic
 
 // TODO: This requires malloc support for the threads states.
+// FIXME: Flaky on all GPU targets.
 // UNSUPPORTED: amdgcn-amd-amdhsa
+// UNSUPPORTED: nvptx64-nvidia-cuda
+// UNSUPPORTED: nvptx64-nvidia-cuda-LTO
 
 #include <omp.h>
 #include <stdio.h>
diff --git a/openmp/libomptarget/test/offloading/info.c b/openmp/libomptarget/test/offloading/info.c
index 81300cc92ec56..da8e4c44c5acc 100644
--- a/openmp/libomptarget/test/offloading/info.c
+++ b/openmp/libomptarget/test/offloading/info.c
@@ -5,6 +5,9 @@
 // RUN: env LIBOMPTARGET_INFO=63 %libomptarget-run-amdgcn-amd-amdhsa 2>&1 | \
 // RUN:   %fcheck-amdgcn-amd-amdhsa -allow-empty -check-prefixes=INFO,AMDGPU
 
+// FIXME: Fails due to optimized debugging in 'ptxas'.
+// UNSUPPORTED: nvptx64-nvidia-cuda-LTO
+
 #include <omp.h>
 #include <stdio.h>
 
diff --git a/openmp/libomptarget/test/offloading/std_complex_arithmetic.cpp b/openmp/libomptarget/test/offloading/std_complex_arithmetic.cpp
index 44f87ad732bfb..641b849bbc3e6 100644
--- a/openmp/libomptarget/test/offloading/std_complex_arithmetic.cpp
+++ b/openmp/libomptarget/test/offloading/std_complex_arithmetic.cpp
@@ -6,6 +6,7 @@
 // FIXME: This fails to link due to missing math symbols. We should provide the
 //        needed math functions in the GPU `libm` and require the GPU C library.
 // UNSUPPORTED: amdgcn-amd-amdhsa
+// UNSUPPORTED: nvptx64-nvidia-cuda-LTO
 
 #include <cassert>
 #include <complex>
diff --git a/openmp/libomptarget/test/unified_shared_memory/close_enter_exit.c b/openmp/libomptarget/test/unified_shared_memory/close_enter_exit.c
index ec292c857f9c7..71be4c9177b06 100644
--- a/openmp/libomptarget/test/unified_shared_memory/close_enter_exit.c
+++ b/openmp/libomptarget/test/unified_shared_memory/close_enter_exit.c
@@ -4,7 +4,10 @@
 // UNSUPPORTED: clang-6, clang-7, clang-8, clang-9
 
 // Fails on amdgpu with error: GPU Memory Error
+// Fails on nvptx with error: an illegal memory access was encountered
 // XFAIL: amdgcn-amd-amdhsa
+// XFAIL: nvptx64-nvidia-cuda
+// XFAIL: nvptx64-nvidia-cuda-LTO
 
 #include <omp.h>
 #include <stdio.h>
diff --git a/openmp/libomptarget/test/unified_shared_memory/close_modifier.c b/openmp/libomptarget/test/unified_shared_memory/close_modifier.c
index 47902a9a298dd..7ca815db3ad82 100644
--- a/openmp/libomptarget/test/unified_shared_memory/close_modifier.c
+++ b/openmp/libomptarget/test/unified_shared_memory/close_modifier.c
@@ -4,7 +4,10 @@
 // UNSUPPORTED: clang-6, clang-7, clang-8, clang-9
 
 // amdgpu runtime crash
+// Fails on nvptx with error: an illegal memory access was encountered
 // UNSUPPORTED: amdgcn-amd-amdhsa
+// UNSUPPORTED: nvptx64-nvidia-cuda
+// UNSUPPORTED: nvptx64-nvidia-cuda-LTO
 
 #include <omp.h>
 #include <stdio.h>
diff --git a/openmp/libomptarget/test/unified_shared_memory/shared_update.c b/openmp/libomptarget/test/unified_shared_memory/shared_update.c
index 3923b89bba4f6..65db9e4f6bdce 100644
--- a/openmp/libomptarget/test/unified_shared_memory/shared_update.c
+++ b/openmp/libomptarget/test/unified_shared_memory/shared_update.c
@@ -3,7 +3,10 @@
 // REQUIRES: unified_shared_memory
 
 // amdgpu runtime crash
+// Fails on nvptx with error: an illegal memory access was encountered
 // UNSUPPORTED: amdgcn-amd-amdhsa
+// UNSUPPORTED: nvptx64-nvidia-cuda
+// UNSUPPORTED: nvptx64-nvidia-cuda-LTO
 
 #include <omp.h>
 #include <stdio.h>