We present theoretical study of ideal two-dimensional electron–hole (e–h) system in a strong magnetic field. The Bose–Einstein condensation of the correlated pairs takes place on a single particle state with an arbitrary wave vector k in a symmetric two-dimensional model. We show that the ground state energy per one exciton and the chemical potential at low exciton damping rates are nonmonotonic functions versus the value of the filling factor, and they form metastable states of dielectric liquid phase with positive compressibility consisting of the Bose–Einstein condensate of magnetoexcitons and liquid drops. Since the dielectric liquid phase of the Bose condensed excitons with low damping rate corresponds to the relative minima of chemical potential, it is more stable than the e–h metallic liquid phase.