A data sample corresponding to 1.23 million hadronic Z decays collected by the ALEPH detector at LEP has been searched for signals of the production of a non-minimal CP-even Higgs boson h in the reaction e+e- --> hZ*. The h decay modes considered were: those of the minimal standard model Higgs boson, with modified branching ratios; decays into a pair of CP-odd Higgs bosons A; and decays into invisible final states. Only one event was found, a very acoplanar e+e- pair which could originate from the standard model background process e+e- --> e+e-nunuBAR. Upper limits for the cross-section of the reaction e+e- --> hZ* have been derived as a function Of m(h), the mass of the Higgs boson h. In the case of invisible decays, the 95% CL lower limit on m(h) is 65 GeV/c2 for a production cross-section equal to that of a minimal standard model Higgs boson. When combined with previous ALEPH results on the reaction e+e- --> hA, these cross-section upper limits exclude a domain in the (m(h), M(A)) plane of the MSSM such that, if invisible h and A decays can be neglected, 95% CL lower limits of 44 and 21 GeV/c2 result for m(h) and m(A), respectively, independent of the other parameters of the model. RI ANTONELLI, ANTONELLA/C-6238-2011; Buttar, Craig/D-3706-2011; Stahl, Achim/E-8846-2011; Passalacqua, Luca/F-5127-2011; Murtas, Fabrizio/B-5729-2012; St.Denis, Richard/C-8997-2012; Forti, Francesco/H-3035-2011; Ferrante, Isidoro/F-1017-2012