We consider a question related to the kinetic theory of granular materials. The model of hard spheres with inelastic collisions is replaced by a Maxwell model, characterized by a collision frequency independent of the relative speed of colliding particles. Our main result is that, in the space-homogeneous case, a selfsimilar asymptotics holds, as conjectured by Ernst–Brito. The proof holds for any initial distribution function with a finite moment of some order greater than two.