  From an analysis of various types of data obtained in relativistic nuclear
collisions, the following picture has emerged in thermal and hydrodynamical
descriptions: as the fluid expands and cools, particles first undergo a
chemical freeze out at T_ch.~160-200 MeV then a thermal freeze out at
T_th~100-140 MeV. In this paper we show how to incorporate these separate
freeze outs consistently in a hydrodynamical code via a modified equation of
state (general case) or via a modified Cooper-Frye formula (particular case of
T_ch. close to T_th. or few particle species undergoing early chemical
freeze-out). The modified equation of state causes faster cooling and may have
sizable impact on the predicted values of observables.
