This paper is devoted to the numerical approximation of attractors. For general nonautonomous dynamical systems we first introduce a new
type of attractor which includes some classes of noncompact attractors such as
unbounded unstable manifolds. We then adapt two cell mapping algorithms
to the nonautonomous setting and use the computer program GAIO for the
analysis of an explicit example, a two-dimensional system of nonautonomous
difference equations. Finally we present numerical data which indicate a bifurcation of nonautonomous attractors in the Duffing-van der Pol oscillator.