  We consider transient random walks on a strip in a random environment. The
model was introduced by Bolthausen and Goldsheid [Comm. Math. Phys. 214 (2000)
429--447]. We derive a strong law of large numbers for the random walks in a
general ergodic setup and obtain an annealed central limit theorem in the case
of uniformly mixing environments. In addition, we prove that the law of the
"environment viewed from the position of the walker" converges to a limiting
distribution if the environment is an i.i.d. sequence.
