  We study localisation effects of strong disorder on the spectral and
dynamical properties of (matrix and scalar) Schroedinger operators with
non-monotone random potentials, on the d-dimensional lattice. Our results
include dynamical localisation, i.e. exponentially decaying bounds on the
transition amplitude in the mean. They are derived through the study of
fractional moments of the resolvent, which are finite due to
resonance-diffusing effects of the disorder. One of the byproducts of the
analysis is a nearly optimal Wegner estimate. A particular example of the class
of systems covered by our results is the discrete alloy-type Anderson model.
