Tightly moored single-body floating devices are an important class of offshore wave energy converters. Examples are the devices under development at the University of Uppsala, Sweden, and Oregon State University, USA, prototypes of which were recently tested. These devices are equipped with a linear electrical generator. The mooring system consists of a cable that is kept tight by a spring or equivalent device. This cable also prevents the buoy from drifting away by providing a horizontal restoring force. The horizontal and (to a lesser extent) the vertical restoring forces are nonlinear functions of the horizontal and vertical displacements of the buoy, which makes the system a nonlinear one (even if the spring and damper are linear), whose modelling requires a time-domain analysis. Such an analysis is presented, preceded, for comparison purposes, by a simpler frequency-domain approach. Numerical results (motions and absorbed power) are shown for a system consisting of a hemispherical buoy in regular and irregular waves and a tight mooring cable. The power take-off is modelled by a simplified system of a linear spring and a linear damper and also by a system formed by a hydraulic piston and spring. Different scenarios are analysed. (C) 2012 Elsevier Ltd. All rights reserved.