In the present article, we describe what we call Intransparent-Gap Relatives (IGRs) in Japanese. In IGRs, a gap is located within the relative clause, and the head noun appears outside the relative clause. Unlike the standard head-external relatives, the gap in IGRs is not transparently associated with the head noun, but they are mediated through a metonymic relation. We propose a formal account of IGRs in terms of incremental parsing in Dynamic Syntax: an IGR string is processed in a left-to-right manner, and a semantic structure is progressively built up. This account unifies the standard head-external relatives and IGRs, relegating their differences to the ways in which the head noun is parsed and construed against the relative clause structure. Confirmation of this analysis comes from cross-constructional and cross-linguistic considerations. First, the analysis predicts that a metonymic reading is available in relatives but not in other rightward-displacement constructions, such as clefts and postposing. Second, the analysis suggests that IGRs are possible in languages such as Japanese and Korean, where the relative clause is processed before the head noun, but not in languages such as English and French, where the head noun is processed before the relative clause.