  We study the effects of disorder on a system of two coupled chain of strongly
correlated fermions (ladder system), using renormalization group. The stability
of the phases of the pure system is investigated as a function of interactions
both for fermions with spin and spinless fermions. For spinless fermions the
repulsive side is strongly localized whereas the system with attractive
interactions is stable with respect to disorder, at variance with the single
chain case. For fermions with spins, the repulsive side is also localized, and
in particular the d-wave superconducting phase found for the pure system is
totally destroyed by an arbitrarily small amount of disorder. On the other hand
the attractive side is again remarkably stable with respect to localization. We
have also computed the charge stiffness, the localization length and the
temperature dependence of the conductivity for the various phases. In the range
of parameter where d-wave superconductivity would occur for the pure system the
conductivity is found to decrease monotonically with temperature, even at high
temperature, and we discuss this surprising result. For a model with one site
repulsion and nearest neighbor attraction, the most stable phase is an orbital
antiferromagnet . Although this phase has no divergent superconducting
fluctuation it can have a divergent conductivity at low temperature. We argue
based on our results that the superconductivity observed in some two chain
compounds cannot be a simple stabilization of the d-wave phase found for a pure
single ladder. Applications to quantum wires are discussed.

Strongly Correlated Electrons