The results of the first complete survey for 6668-MHz CH3OH and 6035-MHz excited-state OH masers in the Small and Large Magellanic Clouds are presented. A new 6668-MHz CH3OH maser in the Large Magellanic Cloud has been detected towards the star-forming region N 160a, together with a new 6035-MHz excited-state OH maser detected towards N 157a. We also re-observed the previously known 6668-MHz CH3OH masers and the single known 6035-MHz OH maser. Neither maser transition was detected above ~0.13 Jy in the Small Magellanic Cloud. All observations were initially made using the CH3OH Multibeam (MMB) survey receiver on the 64-m Parkes radio telescope as part of the overall MMB project. Accurate positions were measured with the Australia Telescope Compact Array (ATCA). In a comparison of the star formation maser populations in the Magellanic Clouds and our Galaxy, the LMC maser populations are demonstrated to be smaller than their Milky Way counterparts. CH3OH masers are under-abundant by a factor of ~50, whilst OH and H2O masers are a factor of ~10 less abundant than our Galaxy.