The paper outlines the semantics of the Hungarian auxiliary + infinitive structure in the cognitive linguistic framework of R. Langacker and B. Heine. The Hungarian auxiliary + infinitive structure is one way to construe a process in a composite semantic structure that represents the semantic functions of the finite verb in a clause, though in a morphosyntactically more complex and semantically more explicit way. The Hungarian auxiliary profiles (future) tense or modality, and the abstracted temporal relation, a process, while the infinitive comprises most of the semantic content of the whole event structure. Trajector and landmark as schematic participants are represented as shared in the two components. This construction is similar to the finite verb, though event structure, eventhood and schematic participants are not always elaborated to the degree they are in the case of a finite verb. Tense is denoted in a restricted way, and the use of modal auxiliaries is related to force dynamic relations.