Time-frequency representations (TFRs) of otoacoustic emissions (OAEs) provide information simultaneously in time and frequency that may be obscured in waveform or spectral analyses. TFRs were applied to transient-evoked stimulus-frequency (SF) and distortion-product (DP) OAEs to test cochlear model predictions. SFOAEs and DPOAEs were elicited in 18 normal-hearing subjects using gated tones and tone pips. Synchronous spontaneous (SS) OAEs were measured to assess their contributions to SFOAEs and DPOAEs. A common form of TFR of measured OAEs was a collection of frequency-specific components often aligned with SSOAE sites, with each component characterized by one or more brief segments or a single long-duration segment. The spectral envelope of evoked OAEs differed from that of the evoking stimulus. Strong emission regions or cochlear "hot spots" were detected, and sometimes accounted for OAE energy observed outside the stimulus bandwidth. Contributions of hot spots and multiple internal reflections to the OAE, and differences between measured and predicted OAE spectra, increased as stimulus level decreased, consistent with level-dependent changes in the estimated cochlear reflectance. Suppression and frequency-pulling effects between components were observed. A recursive formulation was described for the linear coherent reflection emission theory [Zweig and Shera, J. Acoust. Soc. Am. 98, 2018-2047 (1995)] that is well suited for time-domain calculations.