A gradient-based learning algorithm for the dynamics of continuous-time CNN with nonlinear templates is presented. It is applied in order to find the parameters of CNN that model the dynamics of certain multidimensional nonlinear systems, which are characterized by partial differential equations (PDE). The efficiency of the algorithm is compared to that of a non gradient-based learning procedure we have previously developed. Results for modeling two systems, whose dynamics are determined by nonlinear Klein-Gordon-equations, are discussed in detail.