Large radiative corrections modify the predictions of the minimal supersymmetric extension of the standard model (MSSM) sufficiently for the constraints on this model, formerly derived from the searches for the CP-even h and for the CP-odd A neutral Higgs bosons, to be invalidated. In particular, the new h → AA decay mode has to be considered. The results presented here have been obtained from a data sample corresponding to about 185000 hadronic Z decays collected by the ALEPH experiment at LEP. No indication for any signal of the reactions or e+e− → hA was found. A domain in the (mh,mA) plane is thus excluded at 95% CL in a large class of two-Higgs-doublet models. More restrictive results are derived in the MSSM, with one loop radiative corrections to the Higgs potential taken into account. It is found that mh > 41 GeV/c2 and mA > 20 GeV/c2 at 95% CL when the other parameters of the model are varied in their allowed ranges.