  We study wave transmission through one-dimensional random nonlinear
structures and predict a novel effect resulting from an interplay of
nonlinearity and disorder. We reveal that, while weak nonlinearity does not
change the typical exponentially small transmission in the regime of the
Anderson localization, it affects dramatically the disorder-induced localized
states excited inside the medium leading to {\em bistable} and {\em
nonreciprocal} resonant transmission. Our numerical modelling shows an
excellent agreement with theoretical predictions based on the concept of a
high-Q resonator associated with each localized state. This offers a new way of
all-optical light control employing statistically-homogeneous random media
without regular cavities.
