  In the framework of the thermodynamic perturbation theory for fluids we study
how the phase diagram of an isotropic repulsive soft-core attractive potential,
where a liquid-liquid phase transition exists in addition to the standard
gas-liquid phase transition, changes by varying the parameters of the
potential. We show that existence of the liquid-liquid transition is determined
by the interplay of the parameters of the potential and the structure of a
reference liquid.
