A comparative study of the evolution of the Sun–Jupiter–Asteroid system near the 4:1and 7:2 resonances is performed by means of two techniques that proceed differently from theHamiltonian corresponding to the planar restricted elliptic three-body problem. One technique isbased on the classical Schubart averaging while the other is based on a mapping method in whichthe perturbing part of the Hamiltonian is expanded and the resulting terms are ordered according toa weight function that depends on the powers of eccentricities and the coefficients of the terms. Forthe mapping method the effect of Saturn on the asteroidal evolution is introduced and the degree ofchaos is estimated by means of the Lyapunov time. Both methods are shown to lead to similar resultsand can be considered a suitable tool for describing the evolution of asteroids in the Kirkwood gapand the group corresponding to the 4:1 and 7:2 Jovian resonances, respectively.