This study examines the relationship between the Case of a noun phrase (NP) and its quantificational character. It develops a hypothesis about strong and weak readings of NPs on the one hand, and type of Case assignment on the other, based on two types of structural Cases, strong structural Case, licensed at S-structure, and weak structural Case, licensed at D-structure. Morphological realizations of the distinction between weak and strong Cases are found in Finnish, Turkish, and Inuit. According to the hypothesis that links these two types of structural Cases to different interpretations, an object is considered a generalized quantifier only if it bears strong Case. The theory is further extended by applying it to several linguistic environments. The constructions under discussion are sensitive to either syntactic or semantic restrictions. The study shows that these constructions can be accounted for by both types of restrictions, and offers an analysis of object-scrambling in Dutch; the fact that only NPs on a strong reading can be scrambled is attributed to the type of Case that is licensed at different structural positions at different levels of representation. The assumption that scrambling is an instance of A-movement explains the fact that NPs that bear weak Case cannot scramble, although they can topi calize. The hypothesis concerning the relation between Case and interpretation is furthermore extended to subjects to account for the differences in subject interpretations in standard as well as VP-internal positions in English and Dutch. The theory also explains another instance in which a weak-strong effect plays a role, namely PP-extrapolation in English and Dutch.