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Context. The Small Magellanic Cloud (SMC) hosts many known high-mass X-raybinaries (HMXBs), and all but one (SMC X-1) have a Be companion star. Throughthe calibration and verification phase of eROSITA on board theSpektrum-Roentgen-Gamma (SRG) spacecraft, the Be/X-ray binary XMMUJ010429.4-723136 was in the field of view during observations of the supernovaremnant, 1E0102.2-7219, used as a calibration standard.  Aims. We report timing and spectral analyses of XMMU J010429.4-723136 basedon three eROSITA observations of the field, two of which were performed on 2019November 7-9, with the third on 2020 June 18-19. We also reanalyse the OGLE-IVlight curve for that source in order to determine the orbital period.  Methods. We performed a Lomb-Scargle periodogram analysis to search forpulsations (from the X-ray data) and for the orbital period (from the OGLEdata). X-ray spectral parameters and fluxes were retrieved from the best-fitmodel.  Results. We detect, for the first time, the pulsations of XMMUJ010429.4-723136 at a period of ~164 s, and therefore designate the source asSXP 164. From the spectral fitting, we derive a source flux of ~1x10e-12 ergs-1 cm-2 for all three observations, corresponding to a luminosity of ~4x10e35erg s-1 at the distance of the SMC. Furthermore, reanalysing the OGLE lightcurve, including the latest observations, we find a significant periodic signalthat we believe is likely be the orbital period; at 22.3d, this is shorter thanthe previously reported values. The Swift/XRT light curve, extracted from twolong monitorings of the field and folded at the same period, suggests that amodulation is also present in the X-ray data.

SRG/eROSITA discovery of 164 s pulsations from the SMC Be/X-ray binary XMMU J010429.4-723136