Résumé : A study of b semileptonic decays into D, Dπ± and D*π± final states is presented. The D0, D+ and D*+ mesons are exclusively reconstructed in Z decay data recorded from 1992 to 1995 in the DELPHI experiment at LEP. The overall branching fractions are measured to be: BR(b→ D0ℓ-νℓX) = (7.04 + 0.34 (stat) + 0.36 (syst.exp) + 0.17 (BRD))%, BR(b→ D+ℓ-νℓX) = (2.72 + 0.19 (stat) + 0.16 (syst.exp) + 0.18 (BRD))%, BR(b→ D*+ℓ-νℓX) = (2.75 + 0.17 (stat) + 0.13 (syst.exp) + 0.09 (BRD))%, where the D0 and D+ results include also contributions from D*0 and D*+ decays. A fit to the distribution of the π± impact parameter to the primary interaction vertex provides a measurement of the b semileptonic branching fractions into the D0π±X, D+π±X and D*+π±X final states. Assuming that single pion decay modes of B mesons dominate, the partial rates for B→Dπℓ-νℓ and B→D*πℓ-νℓ have been obtained, corresponding to a total branching fraction: BR(B→Dπℓ-νℓ) +BR(B→D*πℓ-νℓ) = (3.40 + 0.52 (stat) + 0.32 (syst))%. This result agrees well with the observed difference between the total B semileptonic branching fraction and the sum of the B→Dℓ-νℓ and B→D*ℓ-νℓ branching fractions. © 2000 Elsevier Science B.V.