To predict the final eye position in the middle of a saccadic eye movement will require long-range prediction. This dissertation investigated techniques for doing this. Many important results about saccadic eye movements and current prediction techinques were reviewed. New prediction techinques have been developed and tested for real saccadic data in computer. Three block processing predictors, two-point linear predictor (TPLP), five-point quadratic predictor (FPQP), and nine-point cubic predictor (NPCP), were derived based on the matrix approach. A different approach to deriving the TPLP, FPQP, and NPCP based on the difference equation was also developed. The difference equation approach is better than the matrix approach because it is not necessary to compute the matrix inversion. Two polynomial predictors: the polynomial-filter predictor 1 (PFP1), which is a linear combination of a TPLP and an FPQP, and the polynomial-filter predictor 2 (PFP2), which is a linear combination of a TPLP, and FPQP, and an NPCP, were also derived. Two recursive predictors: the recursive-least-square (RLS) predictor and the least-mean-square (LMS) predictor, were derived. Results show that the RLS and LMS predictors perform better than TPLP, FPQP, NPCP, PFP1, and PFP2 in the prediction of saccadic eye movements. A mathematical way of verifying the accuracy of the recursive-least-square predictor was developed. This technique also shows that the RLS predictor can be used to identify a signal. Results show that a sinusoidal signal can be described as a second-order difference equation with coefficients 2cosω and -1. In the same way, a cubic signal can be realized as a fourth-order difference equation with coefficients 4, -6, 4, and -1. A parabolic signal can be written as a third-order difference equation with coefficients 3, -3, and 1. And a triangular signal can be described as a second-order difference equation with coefficients 2 and -1. In this dissertation, all predictors were tested with various signals such as saccadic eye movements, ECG, sinusoidal, cubic, triangular, and parabolic signals. The FFT of these signals were studied and analyzed. Computer programs were written in systems language C and run on UNIX supported minicomputer VAX11/750. Results were discussed and compared to that of short-range prediction problems.