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In this talk,explicit Runge-Kutta methods are investigated for numerical solutions of nonlinear differential equations with multiple first integrals.The concept,ε-preserving is introduced to describe the first integrals being approximately retained.Then a modified version of explicit Runge-Kutta methods is presented.Since the modified Runge-Kutta method is explicit,with respect to the computational effort,it is superior to the implicit numerical methods in literature.The order of the modified Runge-Kutta method is the same as the standard Runge-Kutta method,but it is superior in preserving the first integrals to the standard one.Numerical experiments are provided to illustrate the effectiveness of the modified Runge-Kutta method.