This paper presents a procedure for the dimensioning of ATM backbone networks when a combination of symmetric and asymmetric services is to be supported. The dimensioning procedure is done aiming to minimise the operational and maintenance costs of the network. An optimisation model is presented and the proposed solution is based on Lagrangean Relaxation with Sub-Gradient Optimisation. The dimensioning procedure also deals with multi-hour dimensioning and multi-network provider environments. Multi-hour dimensioning is useful when ATM networks have dynamic reconfiguration capabilities. In this case, resources allocated to each service can be reconfigured at the management plane in specific time instants in order to adapt the allocated resources to the expected traffic needs in different time periods.