  The collisional rates associated with the isotropic velocity moments
$<V^{2r}>$ and the anisotropic moments $<V^{2r}V_i>$ and
$<V^{2r}(V_iV_j-d^{-1}V^2\delta_{ij})>$ are exactly derived in the case of the
inelastic Maxwell model as functions of the exponent $r$, the coefficient of
restitution $\alpha$, and the dimensionality $d$. The results are applied to
the evolution of the moments in the homogeneous free cooling state. It is found
that, at a given value of $\alpha$, not only the isotropic moments of a degree
higher than a certain value diverge but also the anisotropic moments do. This
implies that, while the scaled distribution function has been proven in the
literature to converge to the isotropic self-similar solution in well-defined
mathematical terms, nonzero initial anisotropic moments do not decay with time.
On the other hand, our results show that the ratio between an anisotropic
moment and the isotropic moment of the same degree tends to zero.
