A lower limit on the oscillation frequency of the Bs0s0 system is obtained from approximately four million hadronic Z decays accumulated using the ALEPH detector at LEP from 1991 to 1995. Leptons are combined with opposite sign Ds− candidates reconstructed in seven different decay modes as evidence of semileptonic Bs0 decays. Criteria designed to ensure precise proper time reconstruction select 277Ds−ℓ+ combinations. The initial state of these Bs0 candidates is determined using an algorithm optimized to efficiently utilise the tagging information available for each event. The limit at 95% confidence level on the Bs0s0 oscillation frequency is Δms > 6.6 ps−1. The same data is used to update the measurement of the Bs0 lifetime,τs = 1.54−0.13+0.14 (stat) ± 0.04 (syst) ps.