We apply the averaging method of first order to study maximum number limit cycles ordinary differential systems form ¨x + x = ε (f1(x, y)y f2 (x, y)) , ¨y y (g1(x, y)x g2 where f1(x, y) and g1(x, are real cubic polynomials; f2(x, g2(x, quadratic polynomials. Furthermore is a small parameter.