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About 120 Be/X-ray binaries (BeXBs) are known in the Small Magellanic Cloud (SMC); about half of them are pulsating with periods from a few to hundreds of seconds. SXP 1323 is one of the longest-period pulsars known in this galaxy. Aims. SXP 1323 is in the field of view of a large set of calibration observations that we analyse systematically, focusing on the time analysis, in search of periodic signals. Methods. We analyse all available X-ray observations of SXP 1323 from Suzaku, XMM-Newton, and Chandra, in the time range from 1999 to the end of 2016. 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