Abstract Current models of galaxy formation predict that galaxy pairs of comparable magnitudes should become increasingly rare with decreasing luminosity. This seems at odds with the relatively high frequency of pairings among dwarf galaxies in the Local Group. We use literature data to show that ∼30 per cent of all the satellites of the Milky Way and Andromeda galaxies brighter than MV = −8 are found in likely physical pairs of comparable luminosity. Besides the previously recognized pairings of the Magellanic Clouds and of NGC 147/NGC 185, other candidate pairs include the Ursa Minor and Draco dwarf spheroidals, as well as the And I/And III satellites of M31. These pairs are much closer than expected by chance if the radial and angular distributions of satellites were uncorrelated; in addition, they have very similar line-of-sight velocities and luminosities that differ by less than three magnitudes. In contrast, the same criteria pair fewer than 4 per cent of satellites in N-body/semi-analytic models that match the radial distribution and luminosity function of Local Group satellites. If confirmed in studies of larger samples, the high frequency of dwarf galaxy pairings may provide interesting clues to the formation of faint galaxies in the current cosmological paradigm.