  We derive a set of exact cosmological solutions to the D=4, N=1 supergravity
description of heterotic M-theory. Having identified a new and exact SU(3) Toda
model solution, we then apply symmetry transformations to both this solution
and to a previously known SU(2) Toda model, in order to derive two further sets
of new cosmological solutions. In the symmetry-transformed SU(3) Toda case we
find an unusual "bouncing" motion for the M5 brane, such that this brane can be
made to reverse direction part way through its evolution. This bounce occurs
purely through the interaction of non-standard kinetic terms, as there are no
explicit potentials in the action. We also present a perturbation calculation
which demonstrates that, in a simple static limit, heterotic M-theory possesses
a scale-invariant isocurvature mode. This mode persists in certain asymptotic
limits of all the solutions we have derived, including the bouncing solution.
