The distribution of relaxation times in a glass is very broad. As a result the free energy of a glass slowly approaches its equilibrium value but never reaches it. This slow relaxation explains why, in the hysteresis cyecle, the melting temperature is higher than the solidification temperature. We estimate the width of this hysteresis for a general type of transition into the glassy state. We apply these estimates to the special case of the vortex melting transition and find good agreement with recent experiments.