  The Boltzmann equation for d-dimensional inelastic Maxwell models is
considered to analyze transport properties in spatially inhomogeneous states
close to the simple shear flow. A normal solution is obtained via a
Chapman--Enskog--like expansion around a local shear flow distribution f^{(0)}
that retains all the hydrodynamic orders in the shear rate. The constitutive
equations for the heat and momentum fluxes are obtained to first order in the
deviations of the hydrodynamic field gradients from their values in the
reference state and the corresponding generalized transport coefficients are
{\em exactly} determined in terms of the coefficient of restitution \alpha and
the shear rate a. Since f^{(0)} applies for arbitrary values of the shear rate
and is not restricted to weak dissipation, the transport coefficients turn out
to be nonlinear functions of both parameters a and \alpha. A comparison with
previous results obtained for inelastic hard spheres from a kinetic model of
the Boltzmann equation is also carried out.
