A process is described for purifying liquids by cryogenic sublimation. This process involves solidifying the liquid by reducing the temperature and pressure to below the triple point. Purification is then carried out by direct transformation from the solid to the vapor phase. Because of increased differentials in vapor pressures at the low temperature at which the procedure is carried out, this purification process is highly efficient and is also particularly suitable for liquids that are susceptible to decomposition with ordinary purification procedures requiring elevated temperatures. The procedure is also advantageous in separating azeotropes, structurally similar compounds, as well as treating flammable, hydroscopic, corrosive and fuming compounds.