Biometric authentication has become a popular research topic due to its wide applicability including the prevention of fraud in financial transactions. Handwritten signature verification, in contrast with other biometric based authentication methods such as fingerprint and retinal scanning, has the advantage that it is already widely used to endorse financial transactions. However, very little verification on these signatures is done today in practical scenarios. This paper reports on our ongoing research on automatic, on-line, handwritten signature verification. The hybrid system consists of a Kohonen self-organizing map, which find cluster centers in the training data and Hidden Markov Models, which are trained to model the dynamics of signatures. Our initial results are very promising: The system achieves a 0% false rejection rate and a 13% false acceptance rate.