Movement-based visual signals are widely distributed among animal species. They are used in a variety of contexts including mate-choice, pursuit deterrence, alarm signalling and opponent assessment. Important contributions to general theories of animal communication have been made using lizards as model systems. However, much of this work has focused on the iguanids of North and South America. The agamid lizards of Australia have received little attention even though many species are characterized by complex visual displays. Here we present a detailed description of the push-up display of the Jacky Dragon (Amphibolurus muricatus), which comprises five distinct components, including tail-flicks, foreleg waves, and push-ups. Rival males exchange displays when competing for territory, but little is known about the rules that govern their expression. We set up simulated intrusions in a captive setting to overcome the inherent difficulty in observing these interactions in the field. An 'intruder' housed in a small tank was positioned in front of a larger enclosure containing a 'resident' male. The response of the resident was video-taped for subsequent analysis. We first examined characteristics of the initial display bout and explored sources of variation within and between residents. Measurements included bout duration, the number and hold duration of push-ups, the total number of components, and limb preferences during foreleg waves. Markov analysis was then used to measure serial dependencies among display components. This showed that the push-up display is a semi-Markovian process: the preceding component predicted the next one with high accuracy. The display is highly constrained irrespective of whether the bout was the first or subsequent response to an intruder, and irrespective of substrate, intruder identity and resident identity. These data are an important first step in understanding the design, perception and function of movement-based visual signals in agamid lizards.