The Hamiltonian formalism is applied to a three-layer Earth model composed of a rigid mantle, a fluid outer core and a rigid inner core, with no dissipation of frictional or electromagnetic origin. Analytical expressions for the free nutations are derived in a set of nonsingular canonical variables that allow a much simpler mathematical treatment. They are checked versus numerical solutions and compared with previous results by Mathews et al. <1991a> and Getino and Ferr¿ndiz <1996, 1998a> with complete agreement up to the first order in the ellipticities. ¿ 2001 American Geophysical Union