Yes / This paper presents a study on selective maintenance for multi-state series-parallel systems with economically dependent components. In the selective maintenance problem, the maintenance manager has to decide which components should receive maintenance activities within a finite break between missions. All the system reliabilities in the next operating mission, the available budget and the maintenance time for each component from its current state to a higher state are taken into account in the optimization models. In addition, the components in series-parallel systems are considered to be economically dependent. Time and cost savings will be achieved when several components are simultaneously repaired in a selective maintenance strategy. As the number of repaired components increases, the saved time and cost will also increase due to the share of setting up between components and another additional reduction amount resulting from the repair of multiple identical components. Different optimization models are derived to find the best maintenance strategy for multi-state series-parallel systems. A genetic algorithm is used to solve the optimization models. The decision makers may select different components to be repaired to different working states based on the maintenance objective, resource availabilities and how dependent the repair time and cost of each component are. © 2013 Elsevier Ltd. All rights reserved. / Natural Sciences and Engineering Research Council of Canada (NSERC) and Vietnam International Education Development (VIED)