We present a system for identifying humans by their walking sounds. This problem is also known as acoustic gait recognition. The goal of the system is to analyse sounds emitted by walking persons (mostly the step sounds) and identify those persons. These sounds are characterised by the gait pattern and are influenced by the movements of the arms and legs, but also depend on the type of shoe. We extract cepstral features from the recorded audio signals and use hidden Markov models for dynamic classification. A cyclic model topology is employed to represent individual gait cycles. This topology allows to model and detect individual steps, leading to very promising identification rates. For experimental validation, we use the publicly available TUM GAID database, which is a large gait recognition database containing 3050 recordings of 305 subjects in three variations. In the best setup, an identification rate of 65.5 % is achieved out of 155 subjects. This is a relative improvement of almost 30 % compared to our previous work, which used various audio features and support vector machines.