The Hamiltonian is expanded to the fourth order in eccentricities in the secular formulation of the planar restricted three-body problem. The dynamics of a minor planet in a single secular resonance with a massive perturbing planet in a single-star system is considered. Equilibrium points and their corresponding resonance zones in the phase space of the system are identified. The dependence of the phase-space structure (existence and location of equilibrium points) on the apsidal precession rate of the orbit of the massive perturbing planet is investigated.