Context. Little is known about the interaction between atmospheres and crusts of exoplanets so far, but future space missions and ground-based instruments are expected to detect molecular features in the spectra of hot rocky exoplanets. Aims. We aim to understand the composition of the gas in an exoplanet atmosphere which is in equilibrium with a planetary crust. Methods. The molecular composition of the gas above a surface made of a mixture of solid and liquid materials was determined by assuming phase equilibrium for given pressure, temperature, and element abundances. We study total element abundances that represent different parts of the Earth’s crust (continental crust, bulk silicate Earth, mid oceanic ridge basalt), CI chondrites and abundances measured in polluted white dwarfs. Results. For temperatures between ~600 and ~3500 K, the near-crust atmospheres of all considered total element abundances are mainly composed of H 2 O, CO 2 , and SO 2 and in some cases of O 2 and H 2 . For temperatures ≲500 K, only N 2 -rich or CH 4 -rich atmospheres remain. For ≳3500 K, the atmospheric gas is mainly composed of atoms (O, Na, Mg, and Fe), metal oxides (SiO, NaO, MgO, CaO, AlO, and FeO), and some metal hydroxides (KOH and NaOH). The inclusion of phyllosilicates as potential condensed species is crucial for lower temperatures, as they can remove water from the gas phase below about 700 K and inhibit the presence of liquid water. Conclusions. Measurements of the atmospheric composition could, in principle, characterise the rock composition of exoplanet crusts. H 2 O, O 2 and CH 4 are natural products from the outgassing of different kinds of rocks that had time to equilibrate. These are discussed as biomarkers, but they do emerge naturally as a result of the thermodynamic interaction between the crust and atmosphere. Only the simultaneous detection of all three molecules might be a sufficient biosignature, as it is inconsistent with chemical equilibrium.