Two-image resituation refers to the recovery of the geometric configuration of two stereo images. This involves determining three intrinsic parameters for each image and five relative orientation parameters. We show here that this can be achieved using only the image coordinates of homologous points, and needs no other control information from object space. The approach is based on a thorough analysis of epipolar constraints. The explicit coplanarity equation defined by the intrinsic and relative orientation parameters is recast into a quadratic form whose parameters define a general coplanarity matrix. This matrix in turn can be written as the product of three matrices, two of which are defined by the intrinsic parameters, and one, called the special coplanaraity matrix, is a function of the five relative orientation parameters. This paper presents a practical procedure for computing all these parameters from only image measurements. The basic strategy is first to find approximate values via closed- form solutions, and then to iteratively fine-tune them to precise values. The key steps are: 1) solving for the general coplanarity matrix via a nonlinear least-squares optimization; 2) solving for two focal lengths from the general coplanarity matrix via a closed-form algebraic solution; 3) determining the special coplanarity matrix from the general coplanarity matrix and the focal lengths; 4) determining the relative orientation parameters including three baseline components and three rotation angles vis closed-form solutions; 5) fine-tuning all the explicit parameters via a iterative linearized least-squares solution. Original or improved solutions are developed for most stages of this procedure. Finally, the computational theory is tested numerically.