The Adaptive Time-delay Neural Network (AT N N), a paradigm for training a nonlinear neural network with adaptive time-delays, is described. Both time delays and connection weights are adapted on-line according to a gradient descent approach, with time delays unconstrained with respect to one another, and an arbitrary number of interconnections with different time delays placed between any two processing units. Weight and time-delay adaptations evolve based on inputs and target outputs consisting of spatiotemporal patterns (e.g. multichannel temporal sequences). The AT N N is used to generate circular and figure- eight trajectories, to model harmonic waves, and to do chaotic time series predictions. Its performance outstrips that of the time-delay neural network (T D N N), which has adaptable weights but fixed time delays. Applications to identification and control as well as signal processing and speech recognition are domains to which this type of network can be appropriately applied.