The sliding friction dynamics of hard single asperities on soft polyester surfaces has been studied. Detailed time-resolved measurements of the sliding dynamics are presented. Of particular interest are normal displacements during "stick–slip". Furthermore, the usual transitions from "stick–slip" to steady sliding behaviour are measured for increasing driving speed and increasing driving spring stiffness. Similar transitions were encountered for decreasing asperity radius and increasing normal force, that are taken to reflect the single-asperity nature of the contact. It is argued that the normal component of displacement is crucial for the sliding dynamics. Based on this observation a simple description in a dynamical system is proposed and its relation to rate-and-state formulations discussed. It is concluded that, apart from being relevant for friction and wear of polymers in general, the system is also interesting as a model system for the study of rate-and-state dynamics.