Using about 950 000 hadronic events collected during 1991 and 1992 with the ALEPH detector, the ratios rb =αbs/(αudscs) and ruds =αudss/(αcbs) have been measured in order to test the flavour independence of the strong coupling constant αs. The analysis is based on event-shape variables using the full hadronic sample, two b-quark samples enriched by lepton tagging and lifetime tagging, and a light-quark sample enriched by lifetime antitagging. The combined results are rb = 1.002+/-0.023 and ruds = 0.971 +/- 0.023.