This report documents the algorithms used in the program MIXMOD to analyse mixed pixel data (assuming linear mixing). The report describes the mathematical algorithms rather than acting as a user’s manual for MIXMOD. The algorithms described obtain the desired solutions, quantify the quality of the solution, and estimate error bounds, using a variety of methods. A novel feature is the ability to handle uncertainty in the assumed end-member spectra, which in practice may be the dominant source of error. The report includes a brief literature review to place the work in its broader context (with references to the mathematics of linear systems and other applications of mixture modelling in remote sensing