We have constructed a mesoscopic stochastic model for a synthetic gene network, and studied how the internal noise would influence the genetic oscillations of such a system. We find that the internal noise can play rather constructive roles via a mechanism of internal noise stochastic resonance, i.e., the stochastic genetic oscillations can show best performance at an optimal internal noise level. Since the magnitude of the internal noise is determined by the system size, this phenomenon also demonstrates a kind of system size resonance. (C) 2004 Elsevier B.V. All rights reserved.