This study investigates the applicability of the Subset Principle in the second language (L2) acquisi:ion of the Oblique-Case Parameter by 45 learners of French. First, the Subset Principle is defined and discussed, along with its learnability predictions in first language (L1) acquisition. Then, a brief overview of the relevant literature in L2 acquisition shows that the applicability of the Subset Principle is very much debated. In the present study, the results of a grammaticality judgment task and a correction task provide partial support for the Subset Principle. It seems that the learners have acquired the lack of Exceptional-Case marking and preposition stranding, two of the syntactic properties tested, based on the positive evidence available to them. However, they failed to reject a number of ungrammatical instances of dative alternation and dative passive, leading them to an overgeneralized grammar. It is suggested that L2 learners may need direct or indirect negative evidence to constrain their grammar. Further research is needed to conclude whether the Oblique-Case Parameter really is a parameter of Universal Grammar, and if so, whether adult L2 learners are able to reset their parameters to the proper target language values.