To appear in the Proceedings of "The Golden Age of Cataclysmic Variables (Palermo 2011)", in Mem. Soc. Astron. It. (4 pages, 2 figures)International audienceThe X-ray source XSS J12270-4859 has been first suggested to be a magnetic cataclysmic variable of Intermediate Polar type on the basis of its optical spectrum and a possible 860 s X-ray periodicity. However further X-ray observations by the Suzaku and XMM-Newton satellites did not confirm this periodicity but show a very peculiar variability, including moderate repetitive flares and numerous absorption dips. These characteristics together with a suspected 4.3 h orbital period would suggest a possible link with the so- called "dipping sources", a sub-class of Low-Mass X-ray Binaries (LM...