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This paper describes a fully automated framework to generate realistic head motion, eye gaze, and eyelid motion simultaneously based on live (or recorded) speech input. Its central idea is to learn separate yet interrelated statistical models for each component (head motion, gaze, or eyelid motion) from a prerecorded facial motion data set: 1) Gaussian Mixture Models and gradient descent optimization algorithm are employed to generate head motion from speech features; 2) Nonlinear Dynamic Canonical Correlation Analysis model is used to synthesize eye gaze from head motion and speech features, and 3) nonnegative linear regression is used to model voluntary eye lid motion and log-normal distribution is used to describe involuntary eye blinks. Several user studies are conducted to evaluate the effectiveness of the proposed speech-driven head and eye motion generator using the well-established paired comparison methodology. Our evaluation results clearly show that this approach can significantly outperform the state-of-the-art head and eye motion generation algorithms. In addition, a novel mocap+video hybrid data acquisition technique is introduced to record high-fidelity head movement, eye gaze, and eyelid motion simultaneously.