  We analyze an anisotropic spin 1/2 two legs ladder in the presence of various
type of random perturbations. The generic phase diagram for the pure system, in
a way similar to spin one chains, consists of four phases: an Antiferromagnet,
a Haldane gap or a Singlet phase (depending on the sign of interchain coupling)
and two XY phases designated by XY1 and XY2. The effects of disorder depend
crucially on whether it preserves XY symmetry (random field along z and random
exchange) or not (random anisotropy or random XY fields). The singlet phases
and the massless XY1 phase are totally unaffected by disorder in stark contrast
with the single chain case. On the other hand the XY2 phase is very strongly
suppressed. Disorder breaking XY symmetry has much stronger effects and most of
the phases at the exception of the singlet one are destroyed. Interestingly,
the disordered XY1 phase has a much shorter correlation length than the
disordered XY2 phase contrarily with the case of perturbations preserving the
rotation symmetry around the z axis.
