We consider the discrete one-dimensional quasi-periodic
Schroedinger operator with potential defined by a Gevrey-class function.
We show - in the perturbative regime - that the operator satisfies
Anderson localization and that the Lyapunov exponent is positive and
continuous for all energies. We also mention a partial nonperturbative
result valid for some particular Gevrey classes. These results extend
some recent work by J. Bourgain, M. Goldstein, W. Schlag to a more general
class of potentials.