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 \mathop {\mathgroup \symoperators tan}\nolimits \beta in photon collisions will be presented. Furthermore, \tau ⁺\tau ^- fusion into MSSM Higgs bosons in the photon mode will be shown to give access to the mixing parameter \mathop {\mathgroup \symoperators tan}\nolimits \beta with a precision of better than 10\% for large values of this parameter.

PACS numbers: 12.15.--y, 12.60.--i