Numerous orbits exist in the solar system or in astrodynamics with very peculiar motions. Their common feature is that they consist of two moons or satellites around a much heavier central attractor with almost equal semi-major axes, this is called a co-orbital motion. In spite of analytical theories and numerical investigations developed to describe their long-term dynamics, so far very few rigorous long-time stability results in this setting have been obtained even in the restricted three-body problem. Actually, the nearly equal semi major axes of the moons implies also nearly equal orbital periods (or 1:1 mean motion resonance), and this last point prevent the application of the usual Hamiltonian perturbation theory for the three body problem. Adapting the idea of Arnold to a resonant case, hence by an applcation of KAM theory to the planar planetary three-body problem, we provide a rigorous proof of existence of a large measure set of Lagrangian invariant tori supporting quasi-periodic co-orbital motions, hence stable over infinite times. (Joint work with L. Biasco, L. Chierchia, A. Pousse and P. Robutel) Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023–2027).