Based on the previous work of a number of authors, we discuss an important class of neural networks which we call multi-associative neural networks (MANNs) and which associate one pattern with multiple patterns. As a computationally efficient example of such networks, we describe a specific MANN, that is, a multi-associative, dynamically generated variant of the counterpropagation network (MCPN). As an application of MANNs, we design a general system that can learn and retrieve complex spatio-temporal sequences with any MANN. This system consists of comparator units, a parallel array of MANNs, and delayed feedback lines from the output of the system to the neural network layer. During learning, pairs of sequences of spatial patterns are presented to the system and the system learns-to associate patterns at successive times in sequence. During retrieving, a cue sequence, which may be obscured by spatial noise and temporal gaps, causes the system to output the stored spatio-temporal sequence. We prove analytically that this system is capable of learning and generating any spatio-temporal sequences within the maximum complexity determined by the number of embedded MANNs, with the maximum length and number of sequences determined by the memory capacity of the embedded MANNs. To demonstrate the applicability of this general system, we present an implementation using the MCPN. The system shows desirable properties such as fast and accurate learning and retrieving, and ability to store a large number of complex sequences consisting of nonorthogonal spatial patterns