  The existence of quasi-bi-Hamiltonian structures for the Kepler problem is
studied. We first relate the superintegrability of the system with the
existence of two complex functions endowed with very interesting Poisson
bracket properties and then we prove the existence of a quasi-bi-Hamiltonian
structure by making use of these two functions. The paper can be considered as
divided in two parts. In the first part a quasi-bi-Hamiltonian structure is
obtained by making use of polar coordinates and in the second part a new
quasi-bi-Hamiltonian structure is obtained by making use of the separability of
the system in parabolic coordinates.
