The aim of this paper is to study the dynamics of a floating body with characteristics comparable to a point absorber wave energy converter with different mooring systems, in geometrical configuration or in the materials. To this purpose, the dynamics of a moored buoy is investigated. The point absorber is modeled as a spherical buoy in plane two-dimensional motion, and it is studied under the action of irregular unidirectional wind-generated waves, moored to the seabed by means of one, two or three mooring lines. Two different sets of moorings are considered, and typical wires and chains used in offshore technology are considered, leading to a total of 6 case studies. A quasi-static approach is used for modeling the restoring forces needed to keep buoy into station, using an innovative iterative procedure able to predict for each time instant and for each cable the lay down length of the cable, being each mooring line allowed to be taut or slack. Approaches in the time and frequency domains are used to obtain the system responses in intermediate waters, where these facilities are usually installed. Results for all case studies are compared both in terms of statistics of response and tensions on the top of the cable.