In this paper, we introduce a new concept of associative memories in which synaptic connections of the self-organizing neural network learn time delays between input sequence elements. Synaptic connections represent both the synaptic weights and expected delays between the network inputs. This property of synaptic connections facilitates recognition of time sequences and provides context-based associations between sequence elements. Characteristics of time delays are learned and are updated each time an input sequence is presented. There are no separate learning and testing modes typically used in other neural networks, as the network starts to predict the next input element as soon as there is no expected input signal. The network generates output signals useful for associative recall and prediction. These output signals depend on the presented input context and the knowledge stored in the graph. Such a mode of operation is preferred for the organization of episodic memories used to store the observed episodes and to recall them if a sufficient context is provided. The associative sequential recall is useful for the operation of working memory in a cognitive agent. Test results demonstrate that the network correctly recognizes the input sequences with variable delays and that it is more efficient than other recently developed sequential memory networks based on associative neurons.