  Corrections to the relativistic orbits are studied considering higher order
approximations induced by gravitomagnetic effects. We discuss in details how
such corrections come out taking into account magnetic components in the weak
field limit of gravitational field and then the theory of orbits is developed
starting from the Newtonian one, the lowest order in the approximation.
Finally, the orbital structure and the stability conditions are discussed
giving numerical examples. Beside the standard periastron corrections of
General Relativity, a new nutation effect is due to the c^{-3} corrections. The
transition to a chaotic behavior strictly depends on the initial conditions.
The orbital phase space portrait is discussed.
