Different neural systems are involved in animal navigation depending on the type of task. Experimental studies support the idea that the hippocampus is necessary to learn a spatial representation required to navigate toward hidden goals (place response), whereas the dorsolateral striatum is involved in the learning of stimulus-response associations when navigating toward visible (or cued) goals. These systems compete for action selection according to the characteristics of the task, previous experience (e.g. training procedure) or endogenous factors. This paper reviews both experimental data on the theory of multiple memory systems involved in navigation and a recent computational model of action selection based on the competition of place and cue-responses learnt during training. The model implements separately the two types of response, i.e. place response and stimulus response. Furthermore, competition takes place to select which behaviour will be actually performed. The model was tested in a simulated environment using a protocol analogous to those used in experiments with animals.