Abstract This paper investigates a generative history-based parsing model that synchronises the derivation of non-planar graphs representing semantic dependencies with the derivation of dependency trees representing syntactic structures. To process non-planarity online, the semantic transition-based parser uses a new technique to dynamically reorder nodes during the derivation. While the synchronised derivations allow different structures to be built for the semantic non-planar graphs and syntactic dependency trees, useful statistical dependencies between these structures are modeled using latent variables. The resulting synchronous parser achieves competitive performance on the CoNLL- 2008 shared task, achieving relative error reduction of 12% in semantic F score over previously proposed synchronous models that cannot process non-planarity online