Abstract: This paper mathematiclly derives and theoretically analyses some basic theories of, rotation accuracy of machine tool spindle (such as the mathematical description of spindle error motion, its frequency analysis and the influence of its frequency components on mechanical operation, etc.).For the, further study of various experimental methods of spindle rotation accuracy, especially the treatment method for the experiment date, this paper provides a theoretical base. Also, this paper indicates the defect on the polar coordinates method which is broadly adopted at present, and introduces the basic theorem of cartesian coordinates method.