In this paper the Resource Renting Problem with Overtime (RRP/overtime) is presented. The RRP/overtime is a new problem in which the assumptions of the basic RRP are combined with the possibility to schedule (parts of) activities during overtime. The addition of this extension increases the applicability of the RRP to real world problems. This paper also presents a solution technique for this extension of the resource renting problem. The solution procedure uses a scatter search heuristic to optimize a priority list, which is then in turn used by a schedule generation scheme (PatSGS). A variation on this schedule generation scheme is also used in dedicated local search procedures. The third contribution of this research is a new lower bound for the RRP/overtime problem, which is used to evaluate the results of the proposed heuristic solution method.