Fretting wear and creep can occur simultaneously when two surfaces in contact vibrate against each other at relatively high temperatures. An ability to analyze combined creep and wear is important for applications involving engines, contacting surfaces within fluids of high-temperature heat exchangers, such as fuel rods in nuclear power stations, and contact with polymers close to their glass-transition temperatures. The two phenomena of creep and wear interact with each other through their roles in affecting the shape and stress fields at contacts. Wear is a phenomenon that is generally considered to have no inherent time scale associated with it, beyond the period of the fretting oscillations. Traditional computational models for wear do not require a specific reference to time, but creep models do. Currently, a reliable and efficient numerical algorithm to couple the relatively long time scales of creep to the, generally, short periods of vibrations is not available. In this paper, we present such an algorithm, using an approach of adaptive effective vibration cycles. We demonstrate how to ensure the efficiency and reliability of the modeling by bounding the magnitude of the stress redistribution along the interface during the effective cycle. This approach enables the simulation of problems involving coupled wear and creep. We show that this approach is robust, and that it can be used during full-slip and partial-slip fretting for geometries with smooth or discontinuous interfaces at the edge of the contact. In particular, we use these examples to illustrate some of the crucial roles of creep in wear, such as transitions between partial and full slip.