Negative induced polarization (IP) time-domain transients, sign-changing or non-monotonically decaying transients are currently often considered as measurement errors and removed in the data processing. These transients, here named heterodox in the sense of other than generally accepted signals, might originate from measurement errors, inductive effects, or poor signal processing, but synthetic modelling and field measurements show that these transients are physically possible. A simple theoretical explanation of the basic mechanism for their origin can be found through the superposition of contributions from regions with different sensitivities and such heterodox transients can be identified through the processing of full-waveform IP data. A mathematical classification of orthodox and heterodox IP transients into six different types is introduced based on the temporal development of the sign of their amplitude and derivative. The basic mechanism for IP transients with heterodox shapes is further investigated by considering the subsurface Cole-Cole parameter sensitivities and time-varying IP potential for 2D synthetic models. The time-domain forward response and sensitivities are computed through a time transformation that accounts for the current waveform. This approach allows for quantitative unbiased estimates of the time-domain transients and sensitivities, different from the estimates obtained when using multiple direct-current forward computations, as often done in the inversion of time-domain IP data. Time-domain IP transients may differ from the traditionally expected decaying-like transients when the electrode geometry has IP potential sensitivities with different signs for areas with different IP parameters. Hence, previously disregarded IP transients containing valuable information of the subsurface can be kept for inversion and contribute to the final parameter distribution. Increased understanding of theoretically possible IP transients makes way for more accurate processing of data in the future, reducing the time and resources needed for spectral inversion of time-domain data.