||Offline handwritten signature verification has been used for user identity authentication for a long time. Nowadays, the reliability of this method is being challenged, as skillful forgers can produce forged signatures that cannot be distinguished from genuine ones easily. However, signature verification becomes much more reliable if the online approach is taken by incorporating dynamic features, such as signing pressure, speed, pen-tilt, stroke order and air movement, as these features are "hidden" in the sense that they cannot be revealed by simply observing the shape of the signature. Two different models are commonly used for pattern matching applications. The first one is based on hidden Markov models (HMM) for time-varying patterns and the second one is based on deformable models (DM) for shape-varying patterns. Although HMMs have been demonstrated to be very effective for handwritten character recognition and speech recognition, the statistical nature of HMMs requires that sufficient data be available for model training, which is not a reasonable assumption to take for biometric applications such as signature verification. This calls for the DM approach which does not require many training patterns for model construction. In this thesis, we have performed a number of experiments for the problem of online handwritten signature verification using both the HMM and DM approaches. Experimental results show that the HMM approach is faster and more accurate than the DM approach if the same number of signatures are used for model construction. However, the non-parametric DM approach is more flexible because a reference model can be built from one single signature only, although multiple reference models can be used if more signatures are available for model construction.