We have used the Australia Telescope Compact Array (ATCA) to undertake the first highangular-resolution observations of 37.7-GHz (7−2 →8−1E) methanol masers towards a sample of 11 high-mass star formation regions which host strong 6.7-GHz methanol masers. The 37.7- GHz methanol sites are coincident to within the astrometric uncertainty (0.4 arcsec) with the 6.7-GHz methanol masers associated with the same star formation region. However, spatial and spectral comparison of the 6.7- and 37.7-GHz maser emission within individual sources shows that the 37.7-GHz masers are less often, or to a lesser degree co-spatial than are the 12.2-GHz and 6.7-GHz masers. We also made sensitive, high-angular-resolution observations of the 38.3- and 38.5-GHz class II methanol transitions (62 → 53A− and 62 → 53A+, respectively) and the 36.2-GHz (4−1 → 30E) class I methanol transition towards the same sample of 11 sources. The 37.7-, 38.3-, and 38.5-GHz methanol masers are unresolved in the current observations, which implies a lower limit on the brightness temperature of the strongest masers of more than 106 K. We detected the 38.3-GHz methanol transition towards seven sources, five of which are new detections and detected the 38.5-GHz transition towards six sources, four of which are new detections. We detected 36.2-GHz class I methanol masers towards all 11 sources, 6 of these are new detections for this transition, of which 4 sources do not have previously reported class I methanol masers from any transition.