The hypothesis was tested that learned movement trajectories of different shapes can be stored in, and generated by, largely overlapping neural networks. Indeed, it was possible to train a massively interconnected neural network to generate different shapes of internally stored, dynamically evolving movement trajectories using a general-purpose core part, common to all networks, and a special-purpose part, specific for a particular trajectory. The weights of connections between the core units do not carry any information about trajectories. The core network alone could generate externally instructed trajectories but not internally stored ones, for which both the core and the trajectory-specific part were needed. All information about the movements is stored in the weights of connections between the core part and the specialized units and between the specialized units themselves. Due to these connections the core part reveals specific dynamical behavior for a particular trajectory and, as the result, discriminates different tasks. The percentage of trajectory-specific units needed to generate a certain trajectory was small (2-5%), and the total output of the network is almost entirely provided by the core part, whereas the role of the small specialized parts is to drive the dynamical behavior. These results suggest an efficient and effective mechanism for storing learned motor patterns in, and reproducing them by, overlapping neural networks and are in accord with neurophysiological findings of trajectory-specific cells and with neurological observations of loss of specific motor skills in the presence of otherwise intact motor control.