We have used detailed Monte Carlo simulations to study search strategies for Higgs bosons at high energy ee/sup /minus// colliders. We extend an earlier study of the minimal single-Higgs-doublet model at a center-of-mass energy of 1 TeV to examine the effects of b-quark tagging and jet counting. It is found that these techniques can increase the signal-to-noise ratio substantially in the mass range around the W mass. In addition, we have studied this model at a center-of-mass energy of 400 GeV and found that an ee/sup /minus// collider in this region would be sensitive to a Higgs boson with mass up to twice the Z° mass. We have also considered a nonminimal two-doublet model for the Higgs sector by extending a study of charged Higgs boson searches to include a mass very close to the mass of the W/sup +-/. We demonstrate that techniques which include b-quark tagging can be utilized to extract a significant signal. In addition, we have examined the prospects for detecting nonminimal neutral Higgs bosons at 1 TeV. We conclude that it would be possible to detect the CP-even and CP-odd neutral Higgs bosons when they are pair-produced in e+e/sup /minus// annihilation over a limited mass range. However, in some scenarios of supersymmetry, the charged Higgs boson constitutes a significant background to the CP-odd and the more massive CP-even neutral Higgs boson. 16 refs., 13 figs., 2 tabs.