The two-component unrestricted Hartree-Fock method using relativistic effective core potentials (RECP) with spin-orbit operators 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 RECP including spin-orbit effects. It is possible to estimate differential correlation effects on molecular properties due to the relativistic and/or the spin-orbit interactions at the MP2 level using the present method. Test calculations have been performed for HX and $CH_3X$ (X=Br,I) molecules. Spin-orbit and electron correlation effects affect to dissociation energies and bond lengths of the tested molecules. Espectially, two effects have opposite contributions to dissociation energies.
