This paper reports the results of an experimental study on the accessibility of the UG in L2 learning based on the framework of Wexler and Manzini's (1987) Governing Category Parameter. Subjects are 78 Japanese high school students (low-intermediates and high-intermediates) learning English as a foreign langugage in Japan. The hypothesis is that subjects will have Indirect Access to the UG in the acquisition of English reflexives. The researcher asked subjects' preference for possible and impossible antecedents of reflexives in 36 English sentences. The study showed that the Japanese learners of English can have access to the UG as their English ability develops. Considering the result that high-intermediate learners could show the access more dearly than low-intermediate learners, one can not leave out the role of general problem-solving faculty.