A search for B0s oscillations is performed using a sample of semileptonic b-hadron decays collected by the ALEPH experiment during 1991–95. Compared to previous inclusive lepton analyses, the proper time resolution and b-flavour mistag rate are significantly improved. Additional sensitivity to B0s mixing is obtained by identifying subsamples of events having a B0s purity which is higher than the average for the whole data sample. Unbinned maximum likelihood amplitude fits are performed to derive a lower limit of Δms>9.5ps−1 at the 95% confidence limit (95% CL). Combining with the ALEPH D−s -based analyses yields Δms>9.6ps−1 at 95% CL.