We present the results of the first complete survey of the Large and Small Magellanic Clouds for 6668-MHz methanol and 6035-MHz excited-state hydroxyl masers. In addition to the survey, higher-sensitivity targeted searches towards known star-formation regions were conducted. The observations yielded the discovery of a fourth 6668-MHz methanol maser in the Large Magellanic Cloud (LMC), found towards the star-forming region N160a, and a second 6035-MHz excited-state hydroxyl maser, found towards N157a. We have also re-observed the three previously known 6668-MHz methanol masers and the single 6035-MHz hydroxyl maser. We failed to detect emission from either transition in the Small Magellanic Cloud. All observations were initially made using the Methanol Multibeam (MMB) survey receiver on the 64-m Parkes telescope as part of the MMB project and accurate positions have been measured with the Australia Telescope Compact Array (ATCA). We compare the maser populations in the Magellanic Clouds with those of our Galaxy and discuss their implications for the relative rates of massive star-formation, heavy metal abundance, and the abundance of complex molecules. The LMC maser populations are demonstrated to be smaller than their Milky Way counterparts. Methanol masers are under-abundant by a factor of ~45, whilst hydroxyl and water masers are a factor of ~10 less abundant than our Galaxy.
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