  We consider the generalized almost periodic homogenization problem for two
different types of stochastic conservation laws with oscillatory coefficients
and multiplicative noise. In both cases the stochastic perturbations are such
that the equation admits special stochastic solutions which play the role of
the steady-state solutions in the deterministic case. Specially in the second
type, these stochastic solutions are crucial elements in the homogenization
analysis. Our homogenization method is based on the notion of stochastic
two-scale Young measure, whose existence is established here.
