A comparative review of analytic theories for the motion of Earth satellites in quasicircular orbits written in the spherical coordinate frame is presented. The theory of motion is developed for satellites in quasi-circular and quasi-equatorial orbits subjected to geopotential, luni-solar and solar radiation pressure force perturbations. The intermediate orbit is Keplerian and the equations of motion are solved by the Lyapunov-Poincaré small parameter method. Both resonant and non-resonant cases are considered. The results can be useful for the development of a complete theory of weakly eccentric orbits.