We report the discovery of two binary M dwarf systems in the immediate solar neighbourhood using the Two Micron All Sky Survey (2MASS). The first is an M6.5 companion to the nearby G star HD 86728 (Gl 376). The known properties of HD 86728 indicate that the M dwarf (Gl 376B) is old, metal-rich and only 14.9parsec away. The M dwarf is highly active, with both Hα and X-ray emission. Thus, Gl 376B offers the opportunity to study an old, bright, active M dwarf with known metallicity, age and luminosity. We show that it is probable that Gl 376B is itself an unresolved pair. The other system consists of an M6.5 and an M8 dwarf with 14.5arcsec separation. We estimate a distance of ~16parsec for this very low-mass pair. Stronger activity is observed in the M6.5 dwarf, supporting evidence that chromospheric activity is weakening near the hydrogen-burning limit.