Current research features two different explanations for coordination ellipsis (a type of grammatical ellipsis). The assumption most frequently found there is that these constructions result from omissions of constituents to be filled in when interpreting them. In contrast, in the coupling approach elaborated here the suggestion is that the elliptical part of the construction is directly or indirectly linked with the (supposedly) missing sequence in the non-elliptical part. Relying on constituent grammar and valence grammar we show how this second approach can be validated in theories of grammar. To make this work, the representational foundations of these grammars have to be reorganised in order to solve the theoretical and methodological problems associated with them. This procedure leads, more generally, to new insights concerning the structure and the representation of sentences. Above all, one has to assume two-dimensional structures in which both, the constituent structure and the valence structure generate independent couplings; at the same time, in addition to sequential valence relations parallel valence relations have to be considered.