The goal of this paper is to consider, formulate, and solve prediction problems encountered in tactical air combat. The problem involves prediction and identification of continuous-trajectory air combat maneuvers where only partial/incomplete information is given. This problem is solved using a qualitative representation of the maneuvers and their implementation as a neural network. We have broken our central dynamical problem down into several smaller subproblems ("eigencurves"), which describe the states of a continuous-trajectory dynamic system. We find that the resulting sequences of vectors uniquely express the time evolution of interacting dynamic objects. This method has been used to describe the forms of relationships between accelerations and velocities (not the values themselves.) All possible modes of a system can be identified while offering a complete parametrization of all possible tactical maneuvers. Additional information can be used to establish which of the several alternative behaviors will actually take place. These sequences serve as the symbolic input to the artificial neural network we have provided. We found that due to high correlation of input data, a single hidden layer could not satisfactorily distinguish (with at least 55-85% accuracy) simple one-on-one maneuvers, such as the Turn-In, from more complex two-on-one maneuvers; for this reason, two hidden layers were incorporated. For each layer, many different architectures and learning rules were tested; the network described here gives the best results (55-95% accuracy for partial information). Thus, we found that the neural network implementation provided a high-speed, fault-tolerant, and robust computational cell for the identification of tactical maneuvers and suggestions for a best countermaneuver. We note that, for the sake of completeness, we include considerable background material about neural networks also.