In this paper, we propose an extension to the recursive auto-associative memory (RAAM) by Pollack. This extension, the labelling RAAM (LRAAM), can encode labelled graphs with cycles by representing pointers explicitly. Some technical problems encountered in the RAAM, such as the termination problem in the learning and decoding processes, are solved more naturally in the LRAAM framework. The representations developed for the pointers seem to be robust to recurrent decoding along a cycle. Theoretical and experimental results show that the performances of the proposed learning scheme depend on the way the graphs are represented in the training set. Critical features for the representation are cycles and confluent pointers. Data encoded in a LRAAM can be accessed by a pointer as well as by content. Direct access by content can be achieved by transforming the encoder network of the LRAAM into a particular bidirectional associative memory (BAM). Statistics performed on different instances of LRAAM show a strict connection between the associated BAM and a standard BAM. Different access procedures can be defined depending on the access key. The access procedures are not wholly reliable; however, they seem to have a good success rate. The generalization test for the RAAM is no longer complete for the LRAAM. Some suggestions on how to solve this problem are given. Some results on modular LRAAM, stability and application to neural dynamics control are summarized.