<p>A treatment is given of the spatial restricted elliptic problem of threebodies interacting under Newtonian gravity. The problem depends on two parameters:the ratio between the masses of the main attracting bodies and the eccentricity of theirelliptic orbits. The eccentricity is assumed to be small. Nonlinear equations of motion ofthe test mass near a triangular libration point are analyzed. It is assumed that theparameters of the problem lie on the curves of third-order resonances corresponding tothe planar restricted problem.In addition to these resonances (their number is equal to five), the spatial problemhas a resonance that takes place at any parameter values since thethe frequency of small linear oscillations of the test mass along the axis perpendicular tothe plane of the orbit of the main bodies is equal to the frequency of Keplerian motion ofthese bodies.In this paper, the normal form of the Hamiltonian function of perturbed motionthrough fourth-degree terms relative to deviations from the libration point is obtained.Explicit expressions for the coefficients of normal form up to and including the seconddegree of eccentricity are found.</p>