[en] The lifetimes of the B⁺ and B⁰ mesons, and their ratio, have been measured in the OPAL experiment using 2.4 million hadronic Z⁰ decays recorded at LEP. Z⁰ →bb decays were tagged using displaced secondary vertices and high momentum electrons and muons. The lifetimes were then measured using well-reconstructrd charged and neutral secondary vertices selected in this tagged data sample. The results are τ_B⁺=1.643±0.037±0.025 ps, τ_B⁰=1.523±0.057±0.053 ps, τ_B⁺/τ_B⁰=1.079±0.064±0.041, where in each case the first error is statistical and the second systematic. A larger data sample of 3.1 million hadronic Z⁰ decays has been used for CP and CPT violating effects by comparison of inclusive b and anti b hadron decays. No evidence for such effects is seen. The CP violation parameter Re(ε_B) is measured to be Re(ε _B)=0.001±0.014±0.003 and the fractional difference between b and anti b hadron lifetimes is measured to be (Δτ/τ)_b≡(τ(b-hadron)-τ(anti b-hadron))/τ(average)=0.001±0.012±0.008. (orig.)