We present a general formalism describing the evolution of partially p
olarized light propagating in a medium with cubic nonlinearity. Within
the ergodic approximation we found that totally polarized coherent si
ngle-mode light remains totally polarized, irrespective of the type of
optical medium. Partially polarized light consisting of a mixture of
a coherent component with a random one preserves its degree of polariz
ation in a dissipation-free medium with isotropic nonlinearity, while
only linear or nonlinear dissipation may lead to alteration of the deg
ree of polarization. We also found that in some crystal symmetry point
groups, a time-nonreversible optical response may be the only reason
for an alteration of the degree of polarization.