Maritime surveillance, whether onshore or offshore, is a critical task that requires continuous monitoring of vessels. Authorities rely on a complex combination of information and communication technology systems. Data processing from heterogeneous sources alone is not sufficient, and aerial vehicle deployment in reconnaissance missions is increasingly used to complement these systems. Support for fleet routing decisions is necessary to achieve efficient monitoring of non-characterized vessels. Due to the endurance constraints of flights, the typically large number of diverse objectives with varying priorities, and the fact that the targets are in motion, this problem is formulated as a new variant of routing problem: the Team Orienteering Problem with Moving Targets. Additionally, we consider a heterogeneous fleet of manned and unmanned vehicles, with respective rewards for not using them. An effective MILP formulation is proposed, based on the characterization of graphs for each aerial vehicle. Time is discretized in windows as small as needed for practical accuracy. Each time window, the position of the targets and the vehicles is updated according to their respective speeds. To test the model, we create a dataset with onshore and offshore scenarios. The results demonstrate the value of the proposed approach, the difference behavior between scenarios, and open the way for further research in this area. • A practical case related with a dynamic routing of aerial vehicles for maritime surveillance is presented. • This case is characterized as a generic problem not yet defined in the literature: the Team Orienteering Problem with Moving Targets (TOPMT). • A MILP model is developed to address the proposed problem. • A dataset is constructed and solved with the model to evauate its functionality, effectiveness, and efficiency.