  The Boltzmann equation for inelastic Maxwell models is considered to
determine the velocity moments through fourth degree in the simple shear flow
state. First, the rheological properties (which are related to the
second-degree velocity moments) are {\em exactly} evaluated in terms of the
coefficient of restitution $\alpha$ and the (reduced) shear rate $a^*$. For a
given value of $\alpha$, the above transport properties decrease with
increasing shear rate. Moreover, as expected, the third-degree and the
asymmetric fourth-degree moments vanish in the long time limit when they are
scaled with the thermal speed. On the other hand, as in the case of elastic
collisions, our results show that, for a given value of $\alpha$, the scaled
symmetric fourth-degree moments diverge in time for shear rates larger than a
certain critical value $a_c^*(\alpha)$ which decreases with increasing
dissipation. The explicit shear-rate dependence of the fourth-degree moments
below this critical value is also obtained.
