  We study two models of Anderson-type random operators on two
deterministically coupled continuous strings. Each model is associated with
independent, identically distributed four-by-four symplectic transfer matrices,
which describe the asymptotics of solutions. In each case we use a criterion by
Gol'dsheid and Margulis (i.e. Zariski denseness of the group generated by the
transfer matrices in the group of symplectic matrices) to prove positivity of
both leading Lyapunov exponents for most energies. In each case this implies
almost sure absence of absolutely continuous spectrum (at all energies in the
first model and for sufficiently large energies in the second model). The
methods used allow for singularly distributed random parameters, including
Bernoulli distributions.
