In this paper, we compare two alternative approaches for speaker verification based on hidden Markov model (HMM) technology: single Gaussian HMMs and tied multi-Gaussian HMMs. We tested each system using a database of connected digit strings recorded over local and long-distance telephone lines. According to our experiments, tied-mixture models were able to perform better than the single Gaussian approach provided that sufficient training data were available. Results will be discussed for both text-dependent and text-independent speaker verification.