We report on a general search for neutral and charged Higgs bosons with no assumption that the Higgs sector consists of a single doublet as in the minimal standard model. No signal inconsistent with background is observed in any of the decay channels analysed. From the results of direct searches, model independent limits on Higgs bremsstrahlung and on Higgs pair production from the Z 0 are presented. We interpret the bremsstrahlung limits in the general two-doublet model. Z 0 lineshape measurements further restrict the parameter space available in the two-doublet model. Finally, the results are interpreted in the framework of the minimal supersymmetric extension of the standard model.