Hopf bifurcation problem for artificial compressible systems is considered. The artificial compressible system is obtained by adding the time derivative of the pressure with a small parameter (the artificial Mach number) to the continuity equation of the incompressible Navier-Stokes system. It is shown that if a Hopf bifurcation occurs in the incompressible Navier-Stokes system then so does in the artificial compressible system with small artificial Mach numbers. Convergence of bifurcating solutions as the artificial Mach number goes to zero is also studied for a thermal convection problem. This talk is based on a joint work with Prof. C.-H. Hsia (National Taiwan Univ.), Prof. T. Nishida (Kyoto Univ.) and Dr. Y. Teramoto (Tokyo Tech.).