  We study time-dependent density fluctuations in the stationary state of
driven diffusive systems with two conserved densities $\rho_\lambda$. Using
Monte-Carlo simulations of two coupled single-lane asymmetric simple exclusion
processes we present numerical evidence for universality classes with dynamical
exponents $z=(1+\sqrt{5})/2$ and $z=3/2$ (but different from the
Kardar-Parisi-Zhang (KPZ) universality class), which have not been reported yet
for driven diffusive systems. The numerical asymmetry of the dynamical
structure functions converges slowly for some of the non-KPZ superdiffusive
modes for which mode coupling theory predicts maximally asymmetric $z$-stable
L\'evy scaling functions. We show that all universality classes predicted by
mode coupling theory for two conservation laws are generic: They occur in
two-component systems with nonlinearities in the associated currents already of
the minimal order $\rho_\lambda^2\rho_\mu$. The macroscopic stationary
current-density relation and the compressibility matrix determine completely
all permissible universality classes through the mode coupling coefficients
which we compute explicitly for general two-component systems.
