To comply with the continually growing demand for multimedia content and higher throughputs, the telecom-munication industry has to keep improving the use of the bandwidth resources, leading to the well-known Frequency Assignment Problems (FAP). In this article, we present a new extension of these problems to the case of satellite systems that use a multibeam coverage. With the models we propose, we make sure that for each frequency plan produced there exists a corresponding satellite payload architecture that is cost-efficient and decently complex. Two approaches are presented and compared : a global constraint program that handles all the constraints simultaneously, and a decomposition method that involves both constraint programming and integer linear programming. For the latter approach, we show that the two identified subproblems can respectively be modeled as a multiprocessor scheduling problem and a path-covering problem, and this analogy is used to prove that they both belong to the category of NP-hard problems. We also show that, for the most common class of interference graphs in multibeam satellite systems, the maximal cliques can all be enumerated in polynomial time and their number is relatively low, therefore it is perfectly acceptable to rely on them in the scheduling model that we derived. Our experiments on realistic scenarios show that the decomposition method proposed can indeed provide a solution of the problem when the global CP model does not.