ABSTRACT Almost all dwarf galaxies in the Local Group (LG) that are not satellites of the Milky Way or M 31 belong to either one of two highly symmetric planes. It is still a matter of debate whether these planar structures are dynamically stable or whether they only represent a transient alignment. Proper motions, if they could be measured, could help to discriminate between these scenarios. Such motions could be determined with multi-epoch very long baseline interferometry (VLBI) of sources that show emission from water and methanol at frequencies of 22 and 6.7 GHz, respectively. We report searches for such masers. We have mapped three LG galaxies, NGC 6822, IC 1613, and WLM, in the bands covering the water vapour and methanol lines. These systems are members of the two above-mentioned planes of galaxies. We have produced deep radio continuum (RC) maps and spectral line cubes. The former have been used to identify star-forming regions and to derive global galactic star formation rates (SFRs). These SFRs turn out to be lower than those determined at other wavelengths in two of our sources. This indicates that dwarf galaxies may follow predictions on the RC–SFR relation only in individual regions of enhanced RC emission, but not when considering the entire optical body of the sources. No methanol or water maser emission has been confidently detected, down to line luminosity limits of ∼4 × 10−3 and 10 × 10−3 L⊙, respectively. This finding is consistent with the small sizes, low SFRs, and metallicities of these galaxies.