  We show that it is possible to devise a large class of skew--product
dynamical systems which have strange nonchaotic attractors (SNAs): the dynamics
is asymptotically on fractal attractors and the largest Lyapunov exponent is
nonpositive. Furthermore, we show that quasiperiodic forcing, which has been a
hallmark of essentially allhitherto known examples of such dynamics is {\it
not} necessary for the creation of SNAs.
