Traditionally, the morpheme uy ‘of’ has been treated as a genitive case marker in Korean linguistics. It is thus natural in Korean linguistics that syntactic objects combined with uy are taken to be assigned genitive case. However, some generative grammarians including An (2012) and Hong (2013) have recently defied such tradition by claiming that uy is not a genitive marker but is a prenominal inflection in an allomorphic relation with the so-called adnominal ending (u)n, or by suggesting that those phrases marked with uy are adjuncts rather than specifiers or complements. This study critically examines their claims and analyses, and tries to find out their problems. In doing this, it makes efforts to support the traditional view from which uy is a genitive case marker.