This work deals with the critical inclination problem in artificial satellite theory and the PN effects on it. It is carried out within the domain of Hamiltonian mechanics and is expressed in terms of the Delaunay variables using a perturbation approach based on Lie series and Lie transform and it is modified to suit the application in resonance cases using the Bohlin's technique. The short and long periodic terms are eliminated, and the elements of these transformations are obtained. The secular perturbations are derived and a method is outlined for the computation of position and velocity. Near the critical inclination, the Hamiltonian is reformed so as to consider the PN terms as being of order. The modified technique is applied to perform the long period transformation near the critical inclination. The solution is expressed in terms of elliptic (and like) integrals and elliptic functions. The elements of the transformation are formed and the motion of the perigee is analyzed.
