The lifetimes of the and B− mesons have been measured with the ALEPH detector at LEP. Semileptonic decays of and B− mesons were partially reconstructed by identifying events containing a lepton with an associated meson. The proper time of the B meson was estimated from the measured decay length and the momentum and mass of the D-lepton system. A fit to the proper time of 77 D∗+ℓ− and 77 D0ℓ− candidates, combined with a constraint on the lifetime ratio () arising from the relative rates of observed D∗+ℓ− and D0ℓ− events, yielded the following lifetimes: .