  Proper elements are quasi-integrals of motion, meaning that they can be
considered constant over a certain timespan, and they permit to describe the
long-term evolution with a few parameters. Near-Earth objects (NEOs) generally
have a large eccentricity and therefore they can cross the orbits of the
planets. Moreover, some of them are known to be currently in a mean-motion
resonance with a planet. Thus, the methods previously used for the computation
of main-belt asteroid proper elements are not appropriate for such objects. In
this paper, we introduce a technique for the computation of proper elements of
planet-crossing asteroids that are in a mean-motion resonance with a planet.
First, we numerically average the Hamiltonian over the fast angles while
keeping all the resonant terms, and we describe how to continue a solution
beyond orbit crossing singularities. Proper elements are then extracted from a
frequency analysis of the averaged orbit-crossing solutions. We give proper
elements of some known resonant NEOs, and provide comparisons with non-resonant
models. These examples show that it is necessary to take into account the
effect of the resonance for the computation of accurate proper elements.
