I will present an approach for obtaining pointwise upper bounds for solutions of Boltzmann equations for rarefied gases and granular media. In the elastic collisions case the bounds take the form of Maxwellians, while for the inelastic model in a heat bath we derive a ”stretched exponential” ”3/2” asymptotics. The method is based on a variant of a maximum principle and using the properties of the Carleman form of the collision terms.This is a joint work with I. Gamba, C. Villani and A. Bobylev.