  We develop a rigorous analytical Hamiltonian formalism adapted to the study
of the motion of two planets in co-orbital resonance. By constructing a complex
domain of holomorphy for the planetary Hamilto-nian, we estimate the size of
the transformation that maps this Hamil-tonian to its first order averaged over
one of the fast angles. After having derived an integrable approximation of the
averaged problem, we bound the distance between this integrable approximation
and the averaged Hamiltonian. This finally allows to prove rigorous theorems on
the behavior of co-orbital motions over a finite but large timescale.
