In this research a fuzzy neural network is proposed so, fuzzy mechanism and adaptive neuro fuzzy mechanism are designed and simulated to control the (flow rate) control action on cell multiplexing in (ATM). The cell flow rate on the output of neural- fuzzy controller. Has been simulated depending on the input variables, one of these inputs is the queuing message (message length), the second one is the number of inputs, and third is the type of massage. These input variables are used to build the fuzzy rules uses (FNN) as its condition and the control action as its consequence, combines these rules to represent the model or system. NN is used as a training algorithm to learn the weights of fuzzy system. The simulation process has been executed by using (MATLAB). In the light of this research, it is apparent that NNS and fuzzy logic based systems can play an important role in the control of cell multiplexing in (ATM) network, since they can provide adaptive model free, real time control to the user.