We present results from our Chandra and XMM-Newton observations of two low-luminosity X-ray pulsators SAX J1324.4–6200 and SAX J1452.8–5949 which have spin-periods of 172 s and 437 s respectively . The XMM-Newton spectra for both sources can be fitted well with a simple power-law model of photon index \sim 1.0 . A black-body model can equally well fit the spectra with a temperature of \sim 2 keV for both sources . During our XMM-Newton observations , SAX J1324.4–6200 is detected with coherent X-ray pulsations at a period of 172.86 \pm 0.02 s while no pulsations with a pulse fraction greater than 15 % ( at 98 % confidence level ) are detected in SAX J1452.8–5949 . The spin period of SAX J1324.4–6200 is found to be increasing on a time-scale of \dot { P } = ( 6.34 \pm 0.08 ) \times 10 ^ { -9 } s s ^ { -1 } which would suggest that the accretor is a neutron star and not a white dwarf . Using sub-arcsec spatial resolution of the Chandra telescope , possible counterparts are seen for both sources in the near-infrared images obtained with the SOFI instrument on the New Technology Telescope . The X-ray and near-infrared properties of SAX J1324.4–6200 suggest it to be either a persistent high mass accreting X-ray pulsar or a symbiotic X-ray binary pulsar at a distance \leq 9 kpc . We identify the infrared counterpart of SAX J1452.8–5949 to be a late-type main sequence star at a distance \leq 10 kpc , thus ruling out SAX J1452.8–5949 to be a high mass X-ray binary . However with the present X-ray and near-infrared observations , we can not make any further conclusive conclusion about the nature of SAX J1452.8–5949 .