This paper develops a new iterative technique, based on the concept of fault segmentation and computed using two-dimensional static dislocation theory, to build models of seismic and fault interaction which are physically acceptable and geometrically and kinematically correct. The technique is applied in two steps to seismicity observed at the Middle America Trench. The first step constructs generic models which randomly draw segment strengths and lengths from a two-dimensional probability distribution. The second step constructs predictive models in which segment lengths and strengths are adjusted to mimic the actual geography and timing of large historical earthquakes. Both types of models not only reproduce the statistics of seismicity over five units of magnitude but also duplicate other aspects including foreshock and aftershock sequences, migration of foci, and the capacity to produce both characteristic (when an isolated segment fails) and noncharacteristic earthquakes (when several adjacent or nearby segments fail in concert). Over a period of about 150 years the complex interaction of fault segments and the nonlinear failure conditions conspire to transform an apparently deterministic model into a chaotic one in that small changes in initial conditions ultimately lead to very different patterns of events. At least for the Middle America Trench, it seems doubtful that successful predictive models of earthquakes could span a much longer duration. ¿ American Geophysical Union 1991