The Gemini telescope control system (TCS) uses an integrated pointing/tracking scheme, based on the 'virtual telescope' (VT) concept, but extended to encompass autoguiding and control of the chopping secondary (M2). The TCS treats each autoguider probe as a separate VT, with a different target from the main telescope (namely a guidestar instead of a science source), different color, flexure and so on. The constraint that both the guider VT and the main-telescope VT share one mount (Az,El) enables the (x,y) of the guidestar image to be predicted. Comparisons between the predicted and measured (x,y) positions enable the guiding system to generate rapid adjustments to M2 tip/tilt, taking out windshake as well as other tracking errors. The TCS monitors M2 tip/tilt and adjusts the mount pointing as required, preventing unwanted buildup of M2 offset. Independent control of M2, to accomplish rapid scans while smoothly tracking the (Az,El) mount for example, is provided by having separate 'mount' and 'source' VTs. In this case, the constraint that there is only one mount (Az, El) enables the M2 tip/tilt to be determined which will place the target image in the required place. Chopping is done by implementing the different chop states as different VTs all running in parallel. The TCS is oblivious to the use being made of the different M2 tip/tilts that the different chop states call for, that being left to the various subsystems. The Gemini plan calls for five VTs (two permanent guide detectors and one on-instrument, plus the mount and target VTs), and all but the mount VT support three chop states. Operating at rate of 20 Hz, this means that the entire pointing calculation has to be performed 260 times per second, and some care has been taken to organize the computations efficiently.