  The evolution of two slow--rolling scalar fields with potentials of the form
$V=V_0 \phi^{-\alpha}\exp(-\beta \phi^m)$ is studied. Considering different
values of the parameters $\alpha$, $\beta$ and $m$, we derive several new
inflationary solutions in which one fields just evolves in the background and
is not important for the inflationary dynamics. In addition, we find new
solutions where both fields are dynamically important during inflation.
Moreover, we discuss the evolution of perturbations in both scalar fields and
the spacetime metric, concentrating on the production of entropy perturbations.
We find that for a large region in parameter space and initial conditions
tensor modes are negligible and that adiabatic and isocurvature perturbations
are essentially uncorrelated.
