  Due to the mathematical complexity of the Boltzmann equation for inelastic
hard spheres, a kinetic model has recently been proposed whereby the collision
rate (which is proportional to the relative velocity for hard spheres) is
replaced by an average velocity-independent value. The resulting inelastic
Maxwell model has received a large amount of recent interest, especially in
connection with the high energy tail of homogeneous states. In this paper the
transport coefficients of inelastic Maxwell models in d dimensions are derived
by means of the Chapman-Enskog method for unforced systems as well as for
systems driven by a Gaussian thermostat and by a white noise thermostat.
Comparison with known transport coefficients of inelastic hard spheres shows
that their dependence on inelasticity is captured by the inelastic Maxwell
models only in a mild qualitative way. Paradoxically, a much simpler BGK-like
model kinetic equation is closer to the results for inelastic hard spheres than
the inelastic Maxwell model
