Lindstedt-Poincare Solutions of Clohessy-Wiltshire Equations G. Gomez and M. Marcote Abstract. The purpose of this paper is the semi-analytical computation of the bounded orbits of Hill's equations, describing the relative motion of two particles in their Keplerian motion around a central body. We have considered the case in which one of the particles moves along a circular reference orbit. The solutions obtained are the generalisation of the usual periodic orbits obtained for the linearised equations and also of the third order solution computed by D.L. Richardson and J.W. Mitchell. With the algorithm presented, those orbits can be computed in a fast and efficient way up to a high order in the in-plane and out-off-plane amplitudes.