Ketamine is an NMDA receptor antagonist commonly used to maintain general anesthesia. At anesthetic doses, ketamine causes high power gamma (25-50 Hz) oscillations alternating with slow-delta (0.1-4 Hz) oscillations. These dynamics are readily observed in local field potentials (LFPs) of non-human primates (NHPs) and electroencephalogram (EEG) recordings from human subjects. However, a detailed statistical analysis of these dynamics has not been reported. We characterize ketamine's neural dynamics using a hidden Markov model (HMM). The HMM observations are sequences of spectral power in seven canonical frequency bands between 0 to 50 Hz, where power is averaged within each band and scaled between 0 and 1. We model the observations as realizations of multivariate beta probability distributions that depend on a discrete-valued latent state process whose state transitions obey Markov dynamics. Using an expectation-maximization algorithm, we fit this beta-HMM to LFP recordings from 2 NHPs, and separately, to EEG recordings from 9 human subjects who received anesthetic doses of ketamine. Our beta-HMM framework provides a useful tool for experimental data analysis. Together, the estimated beta-HMM parameters and optimal state trajectory revealed an alternating pattern of states characterized primarily by gamma and slow-delta activities. The mean duration of the gamma activity was 2.2s([1.7,2.8]s) and 1.2s([0.9,1.5]s) for the two NHPs, and 2.5s([1.7,3.6]s) for the human subjects. The mean duration of the slow-delta activity was 1.6s([1.2,2.0]s) and 1.0s([0.8,1.2]s) for the two NHPs, and 1.8s([1.3,2.4]s) for the human subjects. Our characterizations of the alternating gamma slow-delta activities revealed five sub-states that show regular sequential transitions. These quantitative insights can inform the development of rhythm-generating neuronal circuit models that give mechanistic insights into this phenomenon and how ketamine produces altered states of arousal.