  We study the transfer of cosmological perturbations through a nonsingular
cosmological bounce in a special model in which the parameters of the bounce
and the equation of state of matter are chosen such as to allow for an exact
calculation of the evolution of the fluctuations. We find that the growing mode
of the metric fluctuations in the contracting phase goes over into the growing
mode in the expanding phase, a result which is different from what is obtained
in analyses in which fluctuations are matched at a singular hypersurface.
Consequences for Ekpyrotic cosmology are discussed in a limit when the equation
of state of a fluid becomes large.
