  We study the global flow of the anisotropic Manev problem, which describes
the planar motion of two bodies under the influence of an anisotropic Newtonian
potential with a relativistic correction term. We first find all the
heteroclinic orbits between equilibrium solutions. Then we generalize the
Poincare'-Melnikov method and use it to prove the existence of infinitely many
transversal homoclinic orbits. Invoking a variational principle and the
symmetries of the system, we finally detect infinitely many classes of periodic
orbits.
