  During its performance verification phase, the soft X-ray instrument eROSITA
aboard the Spektrum-Roentgen-Gamma(SRG) spacecraft observed large regions in
the Magellanic Clouds, where almost 40 known high-mass X-ray binaries (HMXBs,
including candidates) are located. We looked for new HMXBs in the eROSITA data,
searched for pulsations in HMXB candidates and investigated the long-term
behaviour of the full sample using archival X-ray and optical data. For sources
sufficiently bright, a detailed spectral and temporal analysis of their eROSITA
data was performed. A source detection analysis of the eROSITA images in
different energy bands provided count rates and upper limits for the remaining
sources. We report the discovery of a new Be/X-ray binary in the Large
Magellanic Cloud. The transient SRGEt J052829.5-690345 was detected with a
0.2-8.0 keV luminosity of ~10^35 erg/s and exhibits a hard X-ray spectrum,
typical for this class of HMXBs. The OGLE I-band light curve of the V~15.7 mag
counterpart shows large variations by up to 0.75 mag, which occur quasi
periodically with ~511 days. The eROSITA observations of the Small Magellanic
Cloud covered 16 Be/X-ray binary pulsars, five of them were bright enough to
accurately determine their current pulse period. The pulse periods for SXP 726
and SXP 1323 measured from eROSITA data are ~800 s and ~1006 s, respectively,
far away from their discovery periods. Including archival XMM-Newton
observations we update the spin-period history of the two long-period pulsars
which show nearly linear trends in their period evolution since more than 15
years. The corresponding average spin-down rate for SXP 726 is 4.3 s/yr while
SXP 1323 shows spin-up with a rate of -23.2 s/yr. We discuss the spin evolution
of the two pulsars in the framework of quasi-spherical accretion.
