Two-component models (normal star and degenerate star components) are the simplest realization of clusters with a mass spectrum because the high mass stars quickly evolve off leaving degenerate stars behind, while low mass stars survive for a long time as main-sequence stars. In the present study we examine the post-collapse evolution of globular clusters using two-component Fokker-Planck models that include three-body binary heating. We confirm that a simple parameter ${epsilon}{equiv} (E_{tot}/t_{rh})/(E_c/t_{rc})$ well describes the occurrence of gravothermal oscillations of two-component clusters. Also, we find that the degree of instability depends on the steepness of the mass function such that clusters with a steeper mass function are less exposed to instability.