Résumé : The forward-backward asymmetry of the process e+e-→Z→b {Mathematical expression} has been measured using events collected by the DELPHI experiment during the 1991 and 1992 LEP runs. This data sample corresponded to 884 000 hadronic Z decays at a centre-of-mass energy {Mathematical expression}. The tagging of b-quark events was performed using two approaches; the first was based on the semileptonic decay channels b→X+μ and b→X+e, the second used a lifetime tag with jet-charge reconstruction. The results of these two methods were combined to give {Mathematical expression} With the semileptonic sample, the forward-backward asymmetry of the process e+e-→Z→ {Mathematical expression} was also measured to be {Mathematical expression} The effective value of the Weinberg mixing angle derived from these measurements was {Mathematical expression} © 1995 Springer-Verlag.