We show that it is possible to devise a large class of skew-product dynamic
al systems which have strange nonchaotic attractors (SNAs): the dynamics is
asymptotically on fractal attractors and the largest Lyapunov exponent is
non-positive. Furthermore, we show that quasiperiodic forcing, which has be
en a hallmark of essentially all hitherto known examples of such dynamics i
s not necessary for the creation of SNAs.