This paper investigates a learning system based on growing Radial Basis Function (RBF) networks for acquiring reactive behaviours in mobile robotics. The learning algorithm integrates unsupervised and supervised learning, directly mapping the sensor information to the required motor action. The learning system is evaluated through a number of experiments on a real robot. The experimental results show that our learning system can learn a wide range of robot behaviours from simple tasks to complex tasks and demonstrate that the task need not be known at the programming time. This means that many different behaviours could potentially be acquired by the same learning architecture, thus dramatically reducing the development cost of autonomous robotic systems