Abstract We have used the Australia Telescope Compact Array (ATCA) to make new observations of the 36.2-GHz (4−1 → 30E) methanol transition toward NGC 4945 and NGC 253. These observations have revealed the presence of new maser components toward these galaxies, and have provided the first clear evidence for variability in extragalactic class I methanol masers. Alongside the new observations of NGC 4945 and NGC 253, we present the results of recent 36.2-GHz methanol maser searches toward 12 galaxies, placing upper limits on the emission from the 36.2-GHz class I transition and the 37.7-GHz (72 → 81E) class II maser line toward these sources. Flux density values for the 7-mm continuum emission toward these sources are also reported where applicable. A re-analysis of the published 36.2-GHz methanol observations of Arp 220 undertaken as part of the search revealed some issues with previous imaging procedures. The re-analysis, combined with non-detections in independent follow-up observations suggest that there is no 36.2-GHz methanol emission toward Arp 220 stronger than 3.5 mJy in a 10 km s−1 channel (5σ upper limit).