Theories of grammar typically have some way of accommodating fixed or semi-fixed idiomatic expressions in addition to expressions derived compositionally by general abstract rules. Construction Grammar differs from most other theories in that it takes such idiomatic expressions as a model for the grammar of natural languages as a whole. Linguistic structures at all levels of complexity and schematicity are uniformly modeled as “constructions”, i.e. form-meaning pairs with unpredictable formal or semantic properties. This view of grammar is plausible only to the extent that abstract and complex linguistic structures can be shown to constitute such form-meaning pairs. In this paper, I present an analysis of the so-called “modal infinitives” in German (structures consisting of haben ‘have’ or sein ‘be’ and an infinitive with zu ‘to’). I argue that German modal infinitives can be described adequatlyadequately only if we assume that they are constructions in the sense of Construction Grammar. While their general function of encoding possibility and obligation can be predicted from the meaning of haben/sein and the infinitival verb phrase, at least one of their more specific conventionalized meanings, “obligation without alternatives”, is more specific than anything that could be derived compositionally from these component parts. Since modal infinitives are part of the “core grammar” of German, this analysis strengthens the case for an analysis of natural language grammars in terms of constructions.