The lifetimes of the B-0 and B+ mesons have been measured with the ALE
PH detector at LEP, using approximately 3 million hadronic Z decays co
llected in the period 1991-1994. In the first of three methods, semile
ptonic decays of B-0 and B+ mesons were partially reconstructed by ide
ntifying events containing a lepton with an associated D(-) or (D) ov
er bar(0) meson. The second method used fully reconstructed B-0 and B mesons. The third method, used to measure the B-0 lifetime, employed
a partial reconstruction technique to identify B-0 --> D(-)pi(+)X dec
ays. The combined results are tau(0) = 1.55 +/- 0.06 +/- 0.03 ps, tau(
+) = 1.58 +/- 0.09 +/- 0.03 ps, tau(+)/tau(0) = 1.03 +/- 0.08 +/- 0.02
.