The various search modes for the Higgs bosons of the Standard Model (SM) and
its Minimal Supersymmetric Extension (MSSM) at the International Linear
Collider (ILC) will be summarized briefly. In particular, as a unique discovery
mode the production of heavy neutral MSSM Higgs bosons for medium values of
tanβ in photon collisions will be presented. Furthermore, τ+τ−
fusion into MSSM Higgs bosons in the photon mode will be shown to give access
to the mixing parameter tanβ with a precision of better than 10% for
large values of this parameter.Comment: Proceedings PLC2005, Kazimierz 200