We examine the oscillation and collapse of a relativistic star, e.g., a proto-neutron star, with an equation of state (EOS) which is slowly changing as driven by, e.g., losing of thermal energy through radiations. We find that the frequency of the fundamental mode of oscillation (radial) will gradually increase then abruptly drop to zero when the star gets close to the point of instability. We also find that for a wide range of configurations on the unstable branch of equilibrium configurations, the collapse is dominated by one unstable mode.