Resonant asteroidal motion is investigated over 17 000 years in a three-dimensional elliptical model Sun-Jupiter-Asteroid averaged by Schubart's method à la Poincarè. Orbits remain trapped in the resonance over this period. The various stability mechanisms are discussed. With respect to their behaviour of ω and ῶ, our resulting orbits reveal 5 distinct classes. These 5 classes can be described in Schubart's topology for the planar problem. As compared to the planar case, eccentricities of orbits in the three-dimensional model vary more strongly. This is an important result for the problem of the delivery of meteorites.