A search for doubly-charmed B decays with both charmed mesons reconstructed is performed, using about 3.8 million hadronic Z decays recorded with the ALEPH detector at LEP. A clear signal is observed in the channels B→DsD¯(X) and B→DD¯(X) (where D can be either a D 0 , a D + or a D ∗+ ), providing the first direct evidence for doubly-charmed B decays involving no Ds production. Evidence for associated K0S and K± production in the decays B→DD¯(X) is also presented and some candidates for completely reconstructed decays B→DsD¯(nπ) , B→DD¯K0S and B→DD¯K± are observed. Furthermore, candidates for the two-body Cabibbo suppressed decays B0→D∗−D∗+ and B−→D(∗)0D(∗)− are also observed. Measurements of the corresponding branching fractions are extracted.