Recent computer architectures provide new kinds of on-chip parallelism, including support for multithreading. This trend toward hardware support for multithreading is expected to continue for PC, workstation and high-end architectures. Given the need to find sequences of independent instructions, and the difficulty of achieving this via compiler technology alone, OpenMP could become an excellent means for application developers to describe the parallelism inherent in applications for such architectures. In this paper, we report on several experiments designed to increase our understanding of the behavior of current OpenMP on such architectures. We have tested two different systems: a Sun Fire V490 with Chip Multiprocessor technology and a Dell Precision 450 workstation with Simultaneous MultiThreading technology. OpenMP performance is studied using the EPCC Microbenchmark suite, subsets of the benchmarks in SPEC OMPM2001 and the NAS parallel benchmark 3.0 suites.