  We analyze the large time behavior of a stochastic model for the lay-down of
fibers on a conveyor belt in the production process of nonwovens. It is shown,
that under weak conditions this degenerate diffusion process is strong mixing,
confirming a conjecture of Grothaus and Klar. Moreover, under some additional
assumptions even geometric ergodicity is established using probabilistic tools
-- described in the book of Meyn and Tweedie -- in combination with methods
from stochastic analysis.
