Three-body effects are studied for both asymmetric nuclear matter and pure neutron matter to calculate the nuclear Equation of State (EOS). The Brueckner-Hartree-Fock (BHF) approximation is used using CD BonnB and Argonne V18 potentials. A two-body density dependent Skyrme potential is added to reproduce the empirical saturation point. Good agreement is obtained in comparison with exact calculation including three-body forces.