Evidence of a liquid-liquid equilibrium in simple fluids has recently been
exposed for a density-dependent pair potential in the framework of a van de
r Waals theory. Here this double criticality is investigated by means of co
mputer simulation, a perturbation theory, and integral equation theory. It
is found that the critical point estimated from the integral equation therm
odynamics is not associated with divergent correlations. To cope with these
features, a special simulation procedure, based on the definition of local
densities, is devised. Monte Carlo calculations confirm the existence of t
wo critical points, in agreement with the predictions of perturbation theor
y.