A lattice-Boltzmann simulator of two-phase equilibrium and flow is presented and applications to interface stability problems are discussed. The simulator is based on a lattice-Boltzmann model of nonideal fluids that allows coexistence of two phases of a single substance at an explicitly defined temperature. A set of thermodynamically consistent algorithms is developed to prescribe the equilibrium densities and kinematic viscosities of the vapor and liquid phases of a van der Waals fluid and also the interfacial tension and interfacial thickness. Flow is induced by applying either a constant macroscopic pressure gradient or an external body force. Application to gas displacement by liquid in a pore structure showed that the simulator is capable of reproducing critical flooding phenomena under strong wettability conditions, such as formation of thin films, snap-off in narrow throats, and entrapment of the nonwetting phase.