  The forward-backward asymmetries of the processes e+e- -> Z -> b bbar and
e+e- -> Z -> c cbar were measured from a sample of hadronic Z decays collected
by the DELPHI experiment between 1993 and 1995. Enriched samples of b bbar and
c cbar events were obtained using lifetime information. The tagging of b and c
quarks in these samples was based on the semileptonic decay channels b/c -> X +
mu and b/c -> X + e combined with charge flow information from the hemisphere
opposite to the lepton. Combining the A_{FB}^{b bbar} and A_{FB}^{c cbar}
measurements presented in this paper with published results based on 1991 and
1992 DELPHI data samples, the following pole asymmetries were obtained:
  A_{FB}^{0,b} = 0.1021 +/- 0.0052 (stat) +/- 0.0024 (syst)
  A_{FB}^{0,c} = 0.0728 +/- 0.0086 (stat) +/- 0.0063 (syst)
  The effective value of the weak mixing angle derived from these measurements
is sin^2 theta_{W,eff}^{lept} = 0.23170 +/- 0.00097 .
