Recent progress of understanding of the afterpulse time spectra of high-speed photon detectors using photoemission and secondary emission processes is' reviewed and summarized. Furthermore, the afterpulse time spectra of high-gain conventionally designed and microchannel plate photon detectors has been investigated. Specifically, the devices studied included RCA 8850, RCA 8854 and ITT F 4129f photomultipliers. Descriptions are given of the measuring techniques.