Abstract: This paper deals with the real time problem of determining feasible speed profiles for a number of trains circulating in a given area, compliant with train dynamics and railway safety rules, such that each train is able to reach given points in the network at given times. The results described in this paper are part of a research project on train traffic control systems, supported by the European Commission. Other results of the project include the development of new optimization models and algorithms for traffic management, and a general architecture for train traffic control, capable of managing both fixed block and moving block signalling safety concepts. Computational results are reported, based on a portion of the Dutch railway network, on the highspeed line Paris-Brussels-Amsterdam.