Bd0 and Bs0 oscillation is studied using almost a million hadronic Z decays collected by the ALEPH experiment at LEP. Events are selected with two leptons present, on opposite sides of the event and with high transverse momentum. The leptons are expected to be dominantly from b decays; a topological vertexing technique is applied to measure the decay length of the b hadrons, and their momentum is determined using an energy-flow method. The fraction of events in which the leptons have the same charge is studied as a function of the measured decay time, and clear evidence is seen for the time-dependent nature of mixing. The frequency measured for the oscillation corresponds to a mass difference for the Bd0 mass eigenstates Δmd = (3.3−0.4+0.5 ± 0.7) × 10−4 eV/c2. Allowing a second frequency component for the Bs0 a high value for Δms is favoured, leading to the limit Δms > 12 × 10−4 eV/c2 (95% CL), from which (Δm/Γ)s > 2.0 is derived.