************************************************************************* 63015 We propose ASCA observations of three X-ray luminous starburst galaxies. These objects lie at the upper end of the range of X-ray luminosity exhibited by star-forming galaxies. One of the targets is potentially the most X-ray luminous starburst galaxy known. Hard X-ray observations will help reveal the origin of this powerful emission and constrain the possibility that these systems harbour a buried AGN. *************************************************************************