In some languages there are dependencies between grammatical systems, e.g. there may be fewer tense choices in negative than in positive polarity. We examine the direction of dependencies between eight types of grammatical systems, and establish a dependency hierarchy. Polarity is at the top of the hierarchy—the choices available in another system may depend on polarity, but the possibility of positive/negative specification never depends on any of the other systems considered here. Next come systems associated with the predicate (or perhaps with the clause as a whole): tense, aspect, and evidentiality. Next come systems associated with predicate arguments—person, reference classification (covering gender/noun class, classifiers, and human/nonhuman or animate/inanimate); then number. And finally case, which marks the function of a predicate argument. The rationale for this hierarchy is considered. An appendix adds systems of definiteness to the discussion.