  We derive exact quantum expressions for the localization length $L_c$ for
weak disorder in two- and three chain tight-binding systems coupled by random
nearest-neighbour interchain hopping terms and including random energies of the
atomic sites. These quasi-1D systems are the two- and three channel versions of
Dorokhov's model of localization in a wire of $N$ periodically arranged atomic
chains. We find that $L^{-1}_c=N.\xi^{-1}$ for the considered systems with
$N=(1,2,3)$, where $\xi$ is Thouless' quantum expression for the inverse
localization length in a single 1D Anderson chain, for weak disorder. The
inverse localization length is defined from the exponential decay of the
two-probe Landauer conductance, which is determined from an earlier transfer
matrix solution of the Schr\"{o}dinger equation in a Bloch basis. Our exact
expressions above differ qualitatively from Dorokhov's localization length
identified as the length scaling parameter in his scaling description of the
distribution of the participation ratio. For N=3 we also discuss the case where
the coupled chains are arranged on a strip rather than periodically on a tube.
  From the transfer matrix treatment we also obtain reflection coefficients
matrices which allow us to find mean free paths and to discuss their relation
to localization lengths in the two- and three channel systems.
