Résumé : Final results from the DELPHI Collaboration on the lifetime of B + and B0 mesons and the mean b-hadron lifetime, are presented using the data collected at the Z0 peak in 1994 and 1995. Elaborate, inclusive, secondary vertexing methods have been employed to ensure a b-hadron reconstruction with good efficiency. To separate samples of B + and B0 mesons, high performance neural network techniques are used that achieve very high purity signals. The results obtained are: τB+ = 1.624±0.014 (stat)±0.018 (syst)ps τB0 = 1.531±0.021 (stat)±0.031 (syst) ps τ B+/τB0 = 1.060±0.021 (stat)±0.024 (syst) and for the average b-hadron lifetime: τb = 1.570±0.005 (stat)±0.008 (syst) ps.