Hungarian infinitival constructions have both mono-clausal and biclausal properties at the same time. The arguments of the infinitive behave the same way as the arguments of the finite verb do, but the non-finite verb has its own left periphery. After discussing the general description of Hungarian sentence structure and presenting an HPSG analysis for it–including a description of the connection between word order and scope order in the Hungarian left periphery–this paper presents an analysis for Hungarian infinitival constructions. The analysis lexically distinguishes the left peripheral arguments of the infinitive from its complements, and allows the infinitive and its left peripheral arguments to form constituents, while the complements of the infinitive are inherited to the finite verb.