Interpretation of the fast chlorophyll a fluorescence induction is still a subject of continuing discussion. One of the contentious issues is the influence of photosystem I (PSI) activity on the kinetics of the thermal JIP-phase of OJIP rise. To demonstrate this influence, we realized a series of measurements in wheat leaves subjected to PSI photoinactivation by the sequence of red saturation pulses (15,000μmolphotonsm−2s−1 for 0.3s, every 10s) applied in darkness. Such a treatment led to a moderate decrease of maximum quantum efficiency of PSII (by ~8%), but a strong decrease of the number of oxidizable PSI (by ~55%), which considerably limited linear electron transport and CO2 assimilation. Surprisingly, the PSI photoinactivation had low effects on OJIP kinetics of variable fluorescence. In particular, the amplitude of variable fluorescence of IP-step (ΔVIP), which has been considered to be a measure of PSI content, was not decreased, despite the low content of photooxidizable PSI. On the other hand, the slower relaxation of chlorophyll fluorescence after saturation pulse as well as the results of the double-hit method suggest that PSI inactivation treatment led to an increase of the fraction of QB-nonreducing PSII reaction centers. Our results somewhat challenge the mainstream interpretations of JIP-thermal phase, and at least suggest that the IP amplitude cannot serve to estimate reliably the PSI content or the PSI to PSII ratio. Moreover, these results recommend the use of the novel method of PSI inactivation, which might help clarify some important issues needed for the correct understanding of the OJIP fluorescence rise. •Saturation pulse treatment led to a severe inactivation of photosystem I (PSI).•Low content of active PSI strongly limited linear electron flow and CO2 assimilation.•PSI inactivation caused only minor changes of OJIP kinetics of variable fluorescence.•Amplitude of IP-phase of OJIP rise seemed to be independent of PSI content.•PSI inactivation led to a higher fraction of QB-non-reducing PSII reaction centers.