We propose an approach to remote display systems in which the client predicts the screen update events that the server will send and applies them to the screen immediately, thus eliminating the network round-trip time and making the system more responsive in a wide-area or high loss environment. Incorrectly predicted events are undone when the actual events arrive from the server. The approach requires no server or protocol changes, and thus can work with existing systems. Since it is core to the feasibility of such a speculative remote display system, we study the predictability of the events that occur under typical workloads in two extant systems, Windows Remote Desktop and VNC. We find that simple, state-limited Markov models are often able to correctly predict the next event. Based on these results, we design, implement, and evaluate a speculative remote display extension to the VNC client. In our implementation, the end user can trade off between the responsiveness of the display and the level of temporarily displayed incorrect predictions. We evaluate VNC/SRD with two user studies. We conclude by describing design alternatives.