The optimal synthesis of private telecommunication networks subject to multiple nonsimultaneous demands is considered. A model is given for the multiservice network synthesis model with an accurate representation of the conversion and access costs, while maintaining a classical multicommodity flow representation of the network. This is done by increasing the original network to produce an augmented network. Two decomposition methods for solving the network synthesis problem are presented. The first one is a classical Lagrangian relaxation method and the second is a resource-decomposition-type technique. Some preliminary computational results in both cases are presented. These show that the two methods converge within reasonable computation times. The results also demonstrate that the multihour aspect of the synthesis of multiservice networks should be taken into account in order to realize fully the economies that are possible due to the noncoincidence of different types of demands.>