1 Recent theoretical studies on population synchrony have focused on the role of dispersal, environmental correlation and density dependence in single species. Trophic interactions have received less attention. We explored how trophic interactions affect spatial synchrony. 2 We considered a hostâ€“parasitoid coupled map lattice to understand how the selfâ€organizing spatial patterns generated by such dynamics affect synchrony. In particular, we calculated the spatial correlation functions (SCF) associated with travelling waves, spatial chaos and crystal lattices. 3 Travelling waves were associated with cyclic SCF (called secondâ€order SCF) that differed greatly from those seen in spatial chaos or crystal lattices. Such Uâ€shaped patterns of spatial synchrony, which have not been predicted by singleâ€species models, have been reported recently in real data. Thus, the shape of the SCF can provide a test for trophically generated spatiotemporal dynamics. 4 We also calculated the crossâ€correlation function between the parasitoid and the host. Relatively high parasitoid mobility resulted in high withinâ€patch synchrony of the dynamics of the two species. However, with relatively high host mobility, the parasitoid dynamics began to lag spatially behind those of the host. 5 We speculated that this spatial lag between the host and parasitoid is the ultimate source of travelling waves, because the spatial crossâ€correlation in turn affects host dynamics. 6 A new method to estimate the spatial crossâ€correlation function between two species was developed as an integral part of the study.