diff --git a/libcxx/test/libcxx/language.support/support.dynamic/libcpp_deallocate.sh.cpp b/libcxx/test/libcxx/language.support/support.dynamic/libcpp_deallocate.sh.cpp
--- a/libcxx/test/libcxx/language.support/support.dynamic/libcpp_deallocate.sh.cpp
+++ b/libcxx/test/libcxx/language.support/support.dynamic/libcpp_deallocate.sh.cpp
@@ -18,6 +18,10 @@
 // in a link error.
 // XFAIL: use_system_cxx_lib && target={{.+}}-apple-macosx10.{{9|10|11|12}}
 
+// Libcxx when built for z/OS doesn't contain the aligned allocation functions,
+// nor does the dynamic library shipped with z/OS.
+// UNSUPPORTED: target={{.+}}-zos{{.*}}
+
 // AppleClang < 10 incorrectly warns that aligned allocation is not supported
 // even when it is supported.
 // UNSUPPORTED: apple-clang-9
diff --git a/libcxx/test/libcxx/language.support/support.dynamic/new_faligned_allocation.pass.cpp b/libcxx/test/libcxx/language.support/support.dynamic/new_faligned_allocation.pass.cpp
--- a/libcxx/test/libcxx/language.support/support.dynamic/new_faligned_allocation.pass.cpp
+++ b/libcxx/test/libcxx/language.support/support.dynamic/new_faligned_allocation.pass.cpp
@@ -18,6 +18,10 @@
 // in a link error.
 // XFAIL: use_system_cxx_lib && target={{.+}}-apple-macosx10.{{9|10|11|12}}
 
+// Libcxx when built for z/OS doesn't contain the aligned allocation functions,
+// nor does the dynamic library shipped with z/OS.
+// UNSUPPORTED: target={{.+}}-zos{{.*}}
+
 // REQUIRES: -faligned-allocation
 // ADDITIONAL_COMPILE_FLAGS: -faligned-allocation
 
diff --git a/libcxx/test/std/language.support/support.dynamic/new.delete/new.delete.array/delete_align_val_t_replace.pass.cpp b/libcxx/test/std/language.support/support.dynamic/new.delete/new.delete.array/delete_align_val_t_replace.pass.cpp
--- a/libcxx/test/std/language.support/support.dynamic/new.delete/new.delete.array/delete_align_val_t_replace.pass.cpp
+++ b/libcxx/test/std/language.support/support.dynamic/new.delete/new.delete.array/delete_align_val_t_replace.pass.cpp
@@ -25,6 +25,10 @@
 // yet provide aligned new/delete definitions so this test fails to compile/link.
 // XFAIL: LIBCXX-WINDOWS-FIXME
 
+// Libcxx when built for z/OS doesn't contain the aligned allocation functions,
+// nor does the dynamic library shipped with z/OS.
+// UNSUPPORTED: target={{.+}}-zos{{.*}}
+
 #include <new>
 #include <cstddef>
 #include <cstdlib>
diff --git a/libcxx/test/std/language.support/support.dynamic/new.delete/new.delete.array/new_align_val_t.pass.cpp b/libcxx/test/std/language.support/support.dynamic/new.delete/new.delete.array/new_align_val_t.pass.cpp
--- a/libcxx/test/std/language.support/support.dynamic/new.delete/new.delete.array/new_align_val_t.pass.cpp
+++ b/libcxx/test/std/language.support/support.dynamic/new.delete/new.delete.array/new_align_val_t.pass.cpp
@@ -18,6 +18,10 @@
 // UNSUPPORTED: clang-5, clang-6, clang-7
 // XFAIL: use_system_cxx_lib && target={{.+}}-apple-macosx10.{{9|10|11|12|13}}
 
+// Libcxx when built for z/OS doesn't contain the aligned allocation functions,
+// nor does the dynamic library shipped with z/OS.
+// UNSUPPORTED: target={{.+}}-zos{{.*}}
+
 // test operator new
 
 #include <new>
diff --git a/libcxx/test/std/language.support/support.dynamic/new.delete/new.delete.array/new_align_val_t_nothrow.pass.cpp b/libcxx/test/std/language.support/support.dynamic/new.delete/new.delete.array/new_align_val_t_nothrow.pass.cpp
--- a/libcxx/test/std/language.support/support.dynamic/new.delete/new.delete.array/new_align_val_t_nothrow.pass.cpp
+++ b/libcxx/test/std/language.support/support.dynamic/new.delete/new.delete.array/new_align_val_t_nothrow.pass.cpp
@@ -18,6 +18,10 @@
 // UNSUPPORTED: clang-5, clang-6, clang-7
 // XFAIL: use_system_cxx_lib && target={{.+}}-apple-macosx10.{{9|10|11|12|13}}
 
+// Libcxx when built for z/OS doesn't contain the aligned allocation functions,
+// nor does the dynamic library shipped with z/OS.
+// UNSUPPORTED: target={{.+}}-zos{{.*}}
+
 // test operator new (nothrow)
 
 #include <new>
diff --git a/libcxx/test/std/language.support/support.dynamic/new.delete/new.delete.array/new_align_val_t_nothrow_replace.pass.cpp b/libcxx/test/std/language.support/support.dynamic/new.delete/new.delete.array/new_align_val_t_nothrow_replace.pass.cpp
--- a/libcxx/test/std/language.support/support.dynamic/new.delete/new.delete.array/new_align_val_t_nothrow_replace.pass.cpp
+++ b/libcxx/test/std/language.support/support.dynamic/new.delete/new.delete.array/new_align_val_t_nothrow_replace.pass.cpp
@@ -16,6 +16,10 @@
 // UNSUPPORTED: clang-5, clang-6, clang-7
 // XFAIL: use_system_cxx_lib && target={{.+}}-apple-macosx10.{{9|10|11|12|13}}
 
+// Libcxx when built for z/OS doesn't contain the aligned allocation functions,
+// nor does the dynamic library shipped with z/OS.
+// UNSUPPORTED: target={{.+}}-zos{{.*}}
+
 // test operator new nothrow by replacing only operator new
 
 #include <new>
diff --git a/libcxx/test/std/language.support/support.dynamic/new.delete/new.delete.array/new_align_val_t_replace.pass.cpp b/libcxx/test/std/language.support/support.dynamic/new.delete/new.delete.array/new_align_val_t_replace.pass.cpp
--- a/libcxx/test/std/language.support/support.dynamic/new.delete/new.delete.array/new_align_val_t_replace.pass.cpp
+++ b/libcxx/test/std/language.support/support.dynamic/new.delete/new.delete.array/new_align_val_t_replace.pass.cpp
@@ -9,6 +9,10 @@
 // UNSUPPORTED: c++03, c++11, c++14
 // UNSUPPORTED: sanitizer-new-delete
 
+// Libcxx when built for z/OS doesn't contain the aligned allocation functions,
+// nor does the dynamic library shipped with z/OS.
+// UNSUPPORTED: target={{.+}}-zos{{.*}}
+
 // test operator new replacement
 
 #include <new>
diff --git a/libcxx/test/std/language.support/support.dynamic/new.delete/new.delete.single/delete_align_val_t_replace.pass.cpp b/libcxx/test/std/language.support/support.dynamic/new.delete/new.delete.single/delete_align_val_t_replace.pass.cpp
--- a/libcxx/test/std/language.support/support.dynamic/new.delete/new.delete.single/delete_align_val_t_replace.pass.cpp
+++ b/libcxx/test/std/language.support/support.dynamic/new.delete/new.delete.single/delete_align_val_t_replace.pass.cpp
@@ -25,6 +25,10 @@
 // yet provide aligned new/delete definitions so this test fails to compile/link.
 // XFAIL: LIBCXX-WINDOWS-FIXME
 
+// Libcxx when built for z/OS doesn't contain the aligned allocation functions,
+// nor does the dynamic library shipped with z/OS.
+// UNSUPPORTED: target={{.+}}-zos{{.*}}
+
 #include <new>
 #include <cstddef>
 #include <cstdlib>
diff --git a/libcxx/test/std/language.support/support.dynamic/new.delete/new.delete.single/new_align_val_t.pass.cpp b/libcxx/test/std/language.support/support.dynamic/new.delete/new.delete.single/new_align_val_t.pass.cpp
--- a/libcxx/test/std/language.support/support.dynamic/new.delete/new.delete.single/new_align_val_t.pass.cpp
+++ b/libcxx/test/std/language.support/support.dynamic/new.delete/new.delete.single/new_align_val_t.pass.cpp
@@ -18,6 +18,10 @@
 // asan and msan will not call the new handler.
 // UNSUPPORTED: sanitizer-new-delete
 
+// Libcxx when built for z/OS doesn't contain the aligned allocation functions,
+// nor does the dynamic library shipped with z/OS.
+// UNSUPPORTED: target={{.+}}-zos{{.*}}
+
 // test operator new
 
 #include <new>
diff --git a/libcxx/test/std/language.support/support.dynamic/new.delete/new.delete.single/new_align_val_t_nothrow.pass.cpp b/libcxx/test/std/language.support/support.dynamic/new.delete/new.delete.single/new_align_val_t_nothrow.pass.cpp
--- a/libcxx/test/std/language.support/support.dynamic/new.delete/new.delete.single/new_align_val_t_nothrow.pass.cpp
+++ b/libcxx/test/std/language.support/support.dynamic/new.delete/new.delete.single/new_align_val_t_nothrow.pass.cpp
@@ -18,6 +18,10 @@
 // asan and msan will not call the new handler.
 // UNSUPPORTED: sanitizer-new-delete
 
+// Libcxx when built for z/OS doesn't contain the aligned allocation functions,
+// nor does the dynamic library shipped with z/OS.
+// UNSUPPORTED: target={{.+}}-zos{{.*}}
+
 // test operator new (nothrow)
 
 #include <new>
diff --git a/libcxx/test/std/language.support/support.dynamic/new.delete/new.delete.single/new_align_val_t_nothrow_replace.pass.cpp b/libcxx/test/std/language.support/support.dynamic/new.delete/new.delete.single/new_align_val_t_nothrow_replace.pass.cpp
--- a/libcxx/test/std/language.support/support.dynamic/new.delete/new.delete.single/new_align_val_t_nothrow_replace.pass.cpp
+++ b/libcxx/test/std/language.support/support.dynamic/new.delete/new.delete.single/new_align_val_t_nothrow_replace.pass.cpp
@@ -16,6 +16,10 @@
 // UNSUPPORTED: clang-5, clang-6, clang-7
 // XFAIL: use_system_cxx_lib && target={{.+}}-apple-macosx10.{{9|10|11|12|13}}
 
+// Libcxx when built for z/OS doesn't contain the aligned allocation functions,
+// nor does the dynamic library shipped with z/OS.
+// UNSUPPORTED: target={{.+}}-zos{{.*}}
+
 // test operator new nothrow by replacing only operator new
 
 #include <new>
diff --git a/libcxx/test/std/language.support/support.dynamic/new.delete/new.delete.single/new_align_val_t_replace.pass.cpp b/libcxx/test/std/language.support/support.dynamic/new.delete/new.delete.single/new_align_val_t_replace.pass.cpp
--- a/libcxx/test/std/language.support/support.dynamic/new.delete/new.delete.single/new_align_val_t_replace.pass.cpp
+++ b/libcxx/test/std/language.support/support.dynamic/new.delete/new.delete.single/new_align_val_t_replace.pass.cpp
@@ -9,6 +9,10 @@
 // UNSUPPORTED: c++03, c++11, c++14
 // UNSUPPORTED: sanitizer-new-delete
 
+// Libcxx when built for z/OS doesn't contain the aligned allocation functions,
+// nor does the dynamic library shipped with z/OS.
+// UNSUPPORTED: target={{.+}}-zos{{.*}}
+
 // test operator new replacement
 
 #include <new>