We propose a classification of exoplanet atmospheres based on their H, C, O, N element abundances below about 600 K. Chemical equilibrium models were run for all combinations of H, C, N, O abundances, and three types of solutions were found, which are robust against variations of temperature, pressure and nitrogen abundance. Type A atmospheres contain H 2 O, CH 4 , NH 3 and either H 2 or N 2 , but only traces of CO 2 and O 2. Type B atmospheres contain O 2 , H 2 O, CO 2 and N 2 , but only traces of CH 4 , NH 3 and H 2. Type C atmospheres contain H 2 O, CO 2 , CH 4 and N 2 , but only traces of NH 3 , H 2 and O 2. Other molecules are only present in ppb or ppm concentrations in chemical equilibrium, depending on temperature. Type C atmospheres are not found in the solar system, where atmospheres are generally cold enough for water to condense, but exoplanets may well host such atmospheres. Our models show that graphite (soot) clouds can occur in type C atmospheres in addition to water clouds, which can occur in all types of atmospheres. Full equilibrium condensation models show that the outgassing from warm rock can naturally provide type C atmospheres. We conclude that type C atmospheres, if they exist, would lead to false positive detections of biosignatures in exoplanets when considering the coexistence of CH 4 and CO 2 , and suggest other, more robust non-equilibrium markers.