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We analyze the behavior of the argument of pericenter ω2 of an outer particle in the elliptical restricted three-body problem, focusing on the ω2 resonance or inverse Lidov-Kozai resonance. First, we calculate the contribution of the terms of quadrupole, octupole, and hexadecapolar order of the secular approximation of the potential to the outer particle´s ω2 precession rate (dω2 /dτ). Then, we derive analytical criteria that determine the vanishing of the ω2 quadrupole precession rate (dω2/dτ)quad for different values of the inner perturber´s eccentricity e1. Finally, we use such analytical considerations and describe the behavior of ω2 of outer particles extracted from N-body simulations developed in a previous work. Our analytical study indicates that the values of the inclination i2 and the ascending node longitude Ω2 associated with the outer particle that vanish (dω2 /dτ)quad strongly depend on the eccentricity e1 of the inner perturber. In fact, if e1 < 0.25 (>0.40825), (dω2/dτ)quad is only vanished for particles whose Ω2 circulates (librates). For e1 between 0.25 and 0.40825, (dω2 /dτ)quad can be vanished for any particle for a suitable selection of pairs (Ω2 , i2). Our analysis of the N-body simulations shows that the inverse Lidov-Kozai resonance is possible for small, moderate and high values of e1. Moreover, such a resonance produces distinctive features in the evolution of a particle in the (Ω2 , i2 ) plane. In fact, if ω2 librates and Ω2 circulates, the extremes of i2 at Ω2 = 90◦ and270◦ do not reach the same value, while if ω2 and Ω2 librate, the evolutionary trajectory of the particle in the (Ω2, i2) plane evidences an asymmetry respect to i2 = 90◦ . The evolution of ω2 associated with the outer particles of the N-body simulations can be very well explained by the analytical criteria derived in our investigation.p { margin-bottom: 0.25cm; line-height: 120%; }