The rotation of a rigid Earth with the modified Delaunay variables M. Folgueira y M.J. Sevilla Instituto de Astronomia Y Geodesia (UCM-CSIC) Falcultad de Ciencias Matematicas Universidad Complutense. 28040 Madrid Abstract The study of the Earth's rotation is one of the classic and also actual problems of Celestial Mechanics. It's truth that the problem of the rotation of the Earth around its center of mass is far from being closed subject. During three last decades, new theories, with the application of powerful techniques of Celestial Mechanics, have appeared. The most complete and precise theory of precession and nutation available for a rigid Earth is Kinoshita's theory. His study is characterized by the use of Andoyer variables, a moving reference plane and Hori's averaging perturbation method. Also, he develops a very accurate expression for the lunisolar potential using a set of six variables. In the present work, we have adopted Andoyer variables for the description for the Earth's rotation and introduced in the expression of the potential gravitational energy due to the Moon a set of three va riables which describe perfectly the motion of the Moon: the modified Delaunay variables. With this change and following the theory performs by Kinoshita, we present new series to determine the precession and nutation at the first order.