A process is proposed for liquefying a hydrocarbon-rich fraction, especially natural gas, by a) liquefying the hydrocarbon-rich fraction against the coolant mixture of a cooling circuit, b) compressing the coolant mixture in at least two stages, c) partially condensing the compressed coolant mixture at least downstream of the penultimate compressor stage, d) compressing the lower-boiling gas fraction obtained to the final pressure, e) while cooling the first higher-boiling liquid fraction obtained, expanding it (a) to perform cooling and vaporizing it against the hydrocarbon-rich fraction to be cooled, f) partially condensing the coolant mixture fraction compressed to the final pressure and separating the first lower-boiling gas fraction obtained, after partial condensation, into a second lower-boiling gas fraction and a second higher-boiling liquid fraction, and g) liquefying and subcooling the second lower-boiling gas fraction, sub-cooling the second higher-boiling liquid fraction and expanding the two fractions to different temperature levels to perform cooling (b, c), and partly heating and at least partly vaporizing them against the hydrocarbon-rich fraction to be cooled. According to the invention, the composition of the coolant mixture is selected such that the final boiling point (dew point) of the second lower-boiling gas fraction is at a lower temperature than the initial boiling point of the first higher-boiling liquid fraction.