Present and future searches with e+e− colliders for the neutral Higgs bosons of the Minimal Supersymmetric Standard Model — the complete 1-loop analysis

New mass regions unexcluded by direct searches are revealed by an analysis of experimental results from LEP1 using full 1-loop diagrammatic calculations of radiative corrections in the MSSM. Simulations of experimental signal efficiencies and background rejection factors, and full 1-loop calculations are combined to study the sensitivity for neutral Higgs bosons at LEP2 and the NLC. Compared with previous studies based on an Effective Potential Approach, we identify mass regions where the discovery potential depends on the MSSM parameters other than the top and stop masses. We propose our method of interpretation to be adopted by the four LEP experiments for better precision. The possibility of the experimental distinction between the Higgs boson in the MSM and the lightest Higgs boson in the MSSM is discussed for the NLC.