Neutral Higgs bosons of the Standard Model ({\sc SM}) and the Minimal Supersymmetric Standard Model ({\sc MSSM}) were searched for in the data collected in 1999 by the DELPHI experiment at centre-of-mass energies between 191.6 and 201.7~GeV with a total integrated luminosity of 228 pb. These analyses, in combination with our results at lower energies, set 95\% confidence level lower mass bounds on the Standard Model Higgs boson (107.3~GeV/) and on the lightest neutral scalar (85.9~GeV/) and neutral pseudoscalar (86.5~GeV/) Higgs bosons in representative scans of the {\sc MSSM} parameter space. % excluding in the range [0.9-1.6] An extended scan of the {\sc MSSM} parameter space was also performed to test the robustness of these limits.