The purely leptonic decays Ds -> tau nu and Ds -> mu nu are studied in a sample of four million hadronic Z decays collected with the ALEPH detector at the LEP e+e- collider from 1991 to 1995. The branching fractions are extracted from a combination of two analyses, one optimized to select Ds -> tau nu decays with tau -> e nu nubar or mu nu nubar, and the other optimized for Ds-> mu nu decays. The results are used to evaluate the Ds decay constant, within the Standard Model: fDs = [285 +- 19(stat) +- 40 (syst)] MeV