Although the problem of automatic speaker identification has received considerable attention, no work has been made to deal with overlapping speech that involves multiple persons speaking simultaneously. This study proposes two approaches to automatically identify both simultaneous and non-simultaneous speakers in an audio stream. The first approach consists of an overlapping-speech detection component that determines if a test audio recording contains overlapping speech, followed by either a single-speaker identifier or a two-speaker identifier based on Gaussian mixture models. The second approach runs the single-speaker identifier and two-speaker identifier in parallel. Recognizing that the pairs of speakers can be vast in number, we propose using parallel model combination technique to characterize the simultaneous voices of two speakers based on the individual voice of each speaker. Our experiment results demonstrate the feasibility of the proposed approaches.