Future communications satellites can be expected to employ multibeam antennas for both receiving (uplink) and transmitting (downlink). The use of multibeam satellite transmitting antennas raises the question of how to assign the transmitted power and antenna gain to each of theNbeams such that optimum use is made of satellite resources. We refer to this problem as the downlink allocation problem; it is part of the larger problem of allocating all satellite network variables. This concise paper deals with both problems. Specifically, we rigorously formulate and solve the downlink problem for an arbitrary number of beams using the Lagrange multiplier technique for constrained extremal problems. We then discuss procedures for incorporating the optimum downlink allocation results into a complete system allocation.