Many Bantu languages have a system of complex verbal constructions, where several verbal forms combine to describe a single event. Typically, these consist of an auxiliary and a main verb, and often tense-aspect marking and subject agreement is found on both forms. In this paper we develop a parsing-based, Dynamic Syntax analysis of complex verbal constructions in three Bantu languages—Swahili, Rangi and siSwati—and show how concepts of structural underspecification, accumulation of information and contextual update can be harnessed to explain the use of several verbal forms for the building of one semantic structure. At the heart of the analysis is the idea that structure established early in the parse can be ‘re-built’ from subsequent lexical input as long as incrementality and information growth are respected. This correctly predicts the accumulation of tense-aspect information and the fact that multiple subject markers have to be interpreted identically, while maintaining a uniform pronominal analysis of Bantu subject markers. From a comparative perspective, we show that complex verbal constructions result from processes of grammaticalisation, and, especially with reference to the extensive auxiliary system of siSwati, we sketch different processes of lexical change underlying the stages of the grammaticalisation process.