A learning procedure for the dynamics of cellular neural networks (CNN) with nonlinear cell interactions is presented. It is applied in order to find the parameters of CNN that model the dynamics of certain nonlinear systems, which are characterized by partial differential equations (PDE). Values of a solution of the considered PDE for a particular initial condition are taken as the training pattern at only a small number of points in time. Our results demonstrate that CNN obtained with our method approximate the dynamical behaviour of various nonlinear systems accurately. Results for two nonlinear PDE, the Φ⁴-equation and the sine-Gordon equation, are discussed in detail.