A search has been made for a very light Higgs boson in the processes e+e- → e+e-H and e+e- →μ+μ-H using data collected by ALEPH at the LEP e+e- collider at centre of mass energies close to the Z peak. The mass range between 0 and 57 MeV is unambigously excluded at the 95% confidence level. If we combine this with our previously published analysis, the complete range from 0 to 24 GeV is excluded at 95% CL. The search is extended to light Higgs bosons of the minimal supersymmetric standard model, with the result that all possibilities of coupling are excluded for Higgs masses below 3 GeV.