Autonomous underwater vehicles (AUVs) are underwater robots which are able to perform certain tasks without the help of a human operator. The key skill of each AUV is the capability to avoid collisions. To this end, appropriate devices and software are necessary with the potential to detect obstacles and to take proper decisions from the point of view of both the task and safety of the vehicle. The paper presents a neural collision avoidance system (NCAS) designed for the biomimetic autonomous underwater vehicle (BAUV). The NCAS is a component of the path following and collision avoidance system (PFCAS), which as the name implies is responsible for safely leading the vehicle along a desired path with collision avoidance. The task of NCAS is to make decisions regarding vehicle maneuvers in the horizontal plane, but only in the close proximity of the obstacles. It is implemented as an evolutionary artificial neural network designed by means of a neuro-evolutionary technique called assembler encoding with evolvable operations (AEEO). The paper outlines operation and construction of the BAUV as well as the PFCAS, the role of the NCAS in the entire system, and briefly presents AEEO as well as reporting on the experiments performed in simulation.