Pullback convergence has been investigated in numerous papers as an appropriate attraction concept for nonautonomous problems. However, in this paper, it is illustrated through some simple examples that pullback attractors do not give a complete picture of asymptotic behaviour when the nonautonomous dynamical systems that they generate are formulated as processes. It is then shown how the problem can be resolved using a skew product formulation of the nonautonomous dynamical systems when the state space of the driving system is compact.