  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: tau_B+ = 1.624 +/- 0.014 (stat) +/- 0.018 (syst) ps tau_B0 =
1.531 +/- 0.021 (stat) +/- 0.031 (syst) ps tau_B+/tau_B0 = 1.060 +/- 0.021
(stat) +/- 0.024 (syst) and for the average b-hadron lifetime: tau_b = 1.570
+/- 0.005 (stat) +/- 0.008 (syst) ps.
