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Since its launch in 2002, the International Gamma-Ray Astrophysics Laboratory (INTEGRAL) satellite has detected many gamma-ray bursts (GRBs), which are summarised in the INTEGRAL Burst Alert System (IBAS) catalogue. This catalogue combines triggers from the data of the Imager on Board the INTEGRAL (IBIS) and of the anti-coincident shield (ACS) of the SPectrometer on INTEGRAL (SPI). Since the Germanium detectors of SPI also serve as a valuable GRB detector on their own, we present an up-to-date time-resolved catalogue covering all GRBs detected by SPI through the end of 2021 in this work. Thanks to SPI’s high energy coverage (20 keV−8 MeV) and excellent energy resolution, it can improve the modelling of the curvature of the spectrum around the peak and, consequently, it could provide clues on the still unknown emission mechanism of GRBs. We split the SPI light curves of the individual GRBs in time bins of approximately constant signals to determine the temporal evolution of spectral parameters. We tested both the empirical spectral models as well as a physical synchrotron spectral model against the data. For most GRBs, the SPI data cannot constrain the high-energy power law shape above the peak energy, but the parameter distributions for the cut-off power law fits are similar to those of the time-resolved catalogue of gamma-ray burst monitor (GBM) GRBs. We find that a physical synchrotron model can fit the SPI data of GRBs well. While checking against detections of other GRB instruments, we identified one new SPI GRB in the SPI field of view that had not been reported before.