  In this paper we study the evolution of cosmological perturbations through a
nonsingular bouncing universe using covariant perturbation theory and examine
the validity of linear perturbation theory. The bounce is modeled by a two
component perfect fluid. Gauge invariant perturbations are defined in terms of
the comoving observers. The scalar and vector perturbations become singular at
the turning point, which is the boundary of the spacetime region where the null
energy condition is violated. Nonadiabatic modes of comoving curvature
perturbation diverge at the turning point. The gravitational waves oscillate
around the bounce and the turning point. By computing the growth of linearity
parameters, it has been shown that the perturbations do not remain linear at
the turning point. We also study the matching conditions on scalar
perturbations and $\mv$, related to the spatial curvature perturbation, is
found to be the appropriate variable to be matched across transition surface.
