The cohabitation of several different services in the same network raises many problems for the management and the design of telecommunication networks. The introduction of 'intelligent' mechanisms in multiservice networks makes it possible to overcome the difficulty of implementing traditional methods, which take into account all the complexity generated by the multiplication of services. In this context, we focus on the problem of the evaluating performance in network at stationary state, and more specifically the evaluation of the quality of service (QoS) criteria. Instead of trying to model all the mechanisms of a router to formalize certain QoS criteria, we propose to use the training and generalization abilities of neural networks to learn this QoS from observations on the system. We thus propose neuro-mimetic models of various QoS criteria of a network node, which are based on a relatively simple statistical description of incidental traffics. We studied the training of several QoS criteria on discrete-event simulations of elementary queues and time-shared queues modeling service differentiation in IP or MPLS routers. Then, we generalize this approach to carry out the estimation of QoS along a path and propose a distributed cooperation of neural models. The neural networks are in charge to estimate both the quality of service and a description of the outgoing traffic. This scheme coupled with a protocol like RSVP would in the long term make it possible to propagate the estimations along a path to draw up an evaluation of the end-to-end QoS. Finally, we focus on the problem of optimal routing subject to end-to-end QoS constraints. We present a multicommodity flow formalization allowing to set up a flow deviation strategy associated with an augmented Lagrangian approach to relax the QoS constraints. This solving strategy converges to a realizable local optimum. Then, we propose to replace the M/M/1 approximation traditionally used in multicommodity flow models by a neuro-mimetic model of QoS, which is more realistic particularly in case of service differentiation. However, it is necessary to guarantee the growth of the evaluation functions to ensure the validity of the optimization algorithm. This monotonicity can be imposed in the training of the neural model by the addition of constraints on first derivatives. Thus, we develop a constrained training algorithm which takes into account the monotonicity in feed-forward neural networks by using classical algorithm for constrained nonlinear optimization.