The two-component Hartree-Fock method using relativistic effective core potentials (RECP) is extended to include electron correlations by second-order Moller-Plesset perturbation theory (MP2). The present method simultaneously treats electron correlation and all the relativistic effects in REP including spin-orbit effects. It is possible to estimate differential correlation effects on molecular properties due to the relativity and/or the spin-orbit interactions at the MP2 level using the present method. Test calculations have been performed for HX, X2, XY (X, Y = Br, I), and PbH4 molecules. Spin-orbit and electron-correlation effects are rather small for the equilibrium bond lengths and dissociation energies of the tested molecules, but exhibit interesting trends.