In this thesis a study of the theoretical foundations of stellar orbits in non axisymmetric rotating potentials has been made. Before to get into the study of orbits integrated numerically, the linear theory was studied. In this approximation the non-axisymmetry of a potential is taken as a first order perturbation. Using this approximation, the called characteristic curves were built analytically using an isochrone potential. In that way, it was understood how orbits that have been integrated in an inertial frame, closes in a rotating frame to form a characteristic curve. Specifically the GALI2 index and the shooting method were applied in order to build the characteristic curves numerically. These characteristic curves were constructed for a logarithmic potential keeping the pattern speed equal to the unity and varying the axial ratio with values q = 1, q = 0.8, and q = 0.4. The system of differential equations were integrated numerically for 10 Gyrs and our integrator keeps the error in the energy below 10−12 order. In the axisymmetric case (q = 1) all the families of orbits are stable, therefore they keep their morphology for 10 Gyr. In the non-axisymmetric cases it is found that the non-axisymmetry induces chaos on the characteristic curve and some families disappear. The X1 family is found at q = 0.8 and q = 0.4. In both cases this family is stable at lower energies, but some of its members are unstable at higher energies. The stable members of the X1 family are the backbones of the bar structure.