Japanese exhibits the Multiple Nominative Construction (MNC), where more than one nominative-marked NP appear within a single clause. Though the MNC has been extensively investigated in the syntax literature, its relation to rightward-displacement constructions has hardly been discussed. In the present article, we provide new sets of MNC data relating to the three types of right-displacement constructions: relatives, clefts, and postposing. The generalisation is that for the linearly ordered nominative-marked NPs in an MNC string, only the leftmost NP may be (...) right-displaced (that is, relativised, clefted, postposed). This pattern is shown to follow as an outcome of modelling incremental parsing, without stipulations specifically made for the observed data. We propose an account of MNCs in the light of an incremental grammar, formalising it within Dynamic Syntax. In this account, an MNC sentence is parsed on a word-by-word basis, and its interpretation is gradually built up, modelled as the growth of a semantic structure. In cases where a right-displacement is permitted, the right-displaced NP is successfully parsed against the structure built by the preceding part of the sentence. In cases where a right-displacement is disallowed, the right-displaced NP cannot be properly processed because the preceding part of the sentence has created no structural position into which the content of the right-displaced NP is reflected. As theoretical implications of the proposed account, we suggest the concept of time-linear grammaticality. (shrink)