This paper presents high performance speaker identification and verification systems based on Gaussian mixture speaker models: robust, statistically based representations of speaker identification. The identification system is a maximum likelihood classifier and the verification system is a likelihood ratio hypothesis tester using background speaker normalization. The systems are evaluated on four publically available speech databases: TIMIT, NTIMIT, Switchboard and YOHO. The different levels of degradation and variabilities found in these databases allow the examination of system performance for different task domains. Constraints on the speech range from vocabulary-dependent to extemporaneous and speech quality varies from near-ideal, clean speech to noisy, telephone speech. Closed set identification accuracies on the 630 speaker TIMIT and NTIMIT databases were 99.5% and 60.7% respectively. On a 113 speaker population from the Switchboard database the identification accuracy was 82.8%. Global threshold equal error rates of 0.24%, 7.19%, 5.15% and 0.51% were obtained in verification experiments on the TIMIT, NTIMIT, Switchboard and YOHO databases, respectively.