Measurement of the auditory steady-state response (ASSR) is increasingly used to assess marine mammal hearing. These tests normally entail measuring the ASSR to a sequence of sinusoidally amplitude modulated tones, so that the ASSR amplitude function can be defined and the auditory threshold estimated. In this study, an alternative method was employed, where the ASSR was elicited by an amplitude modulated stimulus whose sound pressure level was slowly varied, or "swept," over a range of levels believed to bracket the threshold. The ASSR amplitude function was obtained by analyzing the resulting grand average evoked potential using a short-time Fourier transform. The suitability of this technique for hearing assessment of bottlenose dolphins and California sea lions was evaluated by comparing ASSR amplitude functions and thresholds obtained with swept amplitude and discrete, constant amplitude stimuli. When factors such as the number of simultaneous tones, the number of averages, and the frequency analysis window length were taken into account, the performance and time required for the swept-amplitude and discrete stimulus techniques were similar. The decision to use one technique over another depends on the relative importance of obtaining suprathreshold information versus the lowest possible thresholds.