The trend toward broadband communications in space is foreseeable, and its features predestine ATM as the basic mode of operation. Some of the low and medium earth orbit satellite concepts make use of intersatellite links (ISLs) to provide global connectivity with minimal usage of terrestrial fixed network resources. Interconnecting neighbouring satellites with ISLs results in a partially meshed switching subnetwork in space. The ISLs have a time-varying distance or may even lose sight of each other. This feature of the ISL topology dynamics significantly increases the complexity of connection-oriented network operation and routing. We deal with the routing problem to minimize the virtual path connection handover rate and path delay in the time-varying ISL subnetwork topology with ISL capacity constraints. A heuristic algorithm is proposed to deal with this problem, which is based on Lagrangean relaxation and dynamic programming. When there is sufficient capacity at every ISL, the algorithm an optimal solution easily using only dynamic programming. For evaluation of our algorithm, some computational results have been presented. These results show that our optimization algorithm can produce a solution close to an optimal solution when there exist ISL capacity constraints.