  The present work is devoted to the modelling which is based on the modified
Cahn-Hilliard equation, the interplay of equilibrium and non-equilibrium phase
transitions. The non-equilibrium phase transitions are modelled by the
Schl\"ogl reactions systems. We consider the advancing fronts which combine
these both transitions. The traveling wave solutions are obtained; the
conditions of their existence and dependence on the parameters of the models
are studied in detail. The possibility of the existance of non-equilibrated
phase is discussed.
