Abstract: The Spacetime Constraints (SC) paradigm, whereby the animator specifies what an animated figure should do but not how to do it, is a very appealing approach to animation. However, the algorithms available for realizing the SC approach are limited. Current techniques are local in nature: they all use some kind of perturbational analysis to refine an initial trajectory. We propose a global search algorithm that is capable of generating multiple novel trajectories for SC problems from scratch. The key elements of our search strategy are a method for encoding trajectories as behaviors, and a genetic search algorithm for choosing behavior parameters that is currently implemented on a massively parallel computer. We describe the algorithm and show computed solutions to SC problems for 2D articulated figures.