The ability of humans and animals to quickly adapt to novel tasks is difficult to reconcile with the standard paradigm of learning by slow synaptic weight modification. Here we show that fixed-weight neural networks can learn to generate required dynamics by imitation. After appropriate weight pretraining, the networks quickly and dynamically adapt to learn new tasks and thereafter continue to achieve them without further teacher feedback. We explain this ability and illustrate it with a variety of target dynamics, ranging from oscillatory trajectories to driven and chaotic dynamical systems.