We formulate a general class of neural network based filters, where each node is a morphological/rank operation. This type of system is computationally efficient since no multiplications are necessary. The introduction of such networks is partially motivated from observations that internal structures of a neuron can generate logic operations. An efficient adaptive optimal design procedure is proposed for these networks, based on the back-propagation algorithm. The procedure is optimal under the LMS criterion. Finally, experimental results are illustrated in problems of noise cancellation, encouraging the use of such class of systems and its training algorithm as important tools for nonlinear signal and image processing.