  We prove the propagation of regularity, uniformly in time, for the scaled
solutions of one-dimensional dissipative Maxwell models. This result together
with the weak convergence towards the stationary state proven by Pareschi and
Toscani in 2006 implies the strong convergence in Sobolev norms and in the L^1
norm towards it depending on the regularity of the initial data. In the case of
the one-dimensional inelastic Boltzmann equation, the result does not depend of
the degree of inelasticity. This generalizes a recent result of Carlen,
Carrillo and Carvalho (arXiv:0805.1051v1), in which, for weak inelasticity,
propagation of regularity for the scaled inelastic Boltzmann equation was found
by means of a precise control of the growth of the Fisher information.
