In this paper, the identification of the hydraulic conductivities in a seawater intrusion problem is investigated. The system of two coupled quasilinear partial differential equations describing the direct problem are solved on the basis of an established maximum principle using a fixed point theorem. The existence of an optimal control is proved, even if the conductivities are discontinuous functions, and the necessary conditions for optimality are obtained. Finally, some numerical results are presented for the sake of illustration.