Planets within the habitable zones of M dwarfs are likely to be synchronous rotators; in other words, one side is permanently illuminated while the other side is in perpetual darkness. We present results of three-dimensional simulations of the atmospheres of such planets, and comment on their possible habitability. Near the ground, a thermally direct longitudinal cell exists, transporting heat from the dayside to the nightside. The circulation is three-dimensional, with low-level winds returning mass to the dayside across the polar regions. Aloft, the zonally averaged winds display a pattern of strong superrotation due to these planets' finite (albeit small) rotation rate. With terrestrial values of insolation, a CO2/H2O atmosphere collapses, or condenses on the surface of the darkside, when surface pressure is approximately 30 mb, this value being much lower for a N2atmosphere. This temperature contrast is also sensitive to factors such as gravity, planetary radius, and IR optical depth τ. These results question the suitability of the concept of a habitable zone around M dwarfs that is independent of planetary parameters. If CO2partial pressure is controlled by the carbonate–silicate cycle, we find that these planets should have a minimum surface pressure of 1000–1500 mb of CO2, as this is the minimum pressure needed to support stable liquid water on the darkside at the inner edge of the habitable zone. We finally conclude that planets orbiting M stars can support atmospheres over a large range of conditions and, despite constraints such as stellar activity, are very likely to be habitable.