A search for neutral and charged Higgs bosons has been performed in the data collected by the {\sc DELPHI} detector at centre-of-mass energies of 161~GeV and 172~GeV. The analysis assumes either the pair-production of charged Higgs bosons, H±, or the production of the lightest neutral Higgs boson, h, with either a Z or a neutral pseudoscalar Higgs boson, A. All final state topologies expected from the decay of h and A %neutral Higgs particles into hadrons or a pair of τ leptons, and from the decay of H± %charged Higgs bosons into a pair of quarks or a τντ pair have been considered. %In the case of the associated production with a Z boson, all decay %channels of the Z have been considered. %The case of a %Higgs boson decaying into invisible products has also been studied. %The results are interpreted %in the framework of the Standard Model and of its minimal supersymmetric %extension for the neutral Higgs bosons. %Results for the charged Higgs particles are deduced in the more %general two-doublet scheme. Lower limits at the 95\% confidence level have been obtained on the Higgs boson masses. The limits are 66.2~GeV/c2 for h in the Standard Model, 59.5~GeV/c2 for h and 51.0~GeV/c2 for A in the minimal supersymmetrpseudoscal.