Searches for neutral Higgs bosons produced at LEP in association with Z bosons, in pairs and in the Yukawa process are presented in this paper. Higgs boson decays into b quarks, leptons, or other Higgs bosons are considered, giving rise to four-b, four-b + jets, six-b and four- final states, as well as mixed modes with b quarks and leptons. The whole mass domain kinematically accessible at LEP in these topologies is searched. The analysed data set covers both the LEP1 and LEP2 energy ranges and exploits most of the luminosity recorded by the DELPHI experiment. No convincing evidence for a signal is found, and results are presented in the form of mass-dependent upper bounds on coupling factors (in units of model-independent reference cross-sections) for all processes, allowing interpretation of the data in a large class of models.