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The extensive exploitation of the offshore wave energy resource may require the deployment of dense arrays of point absorbers, the distance between elements being possibly tens of meters. In such cases, it may be more convenient and economical that only elements in the periphery of the array are directly slack-moored to the sea bottom,while the other elements are prevented from drifting and colliding by connections to adjacent elements. Previous work was done in a base configuration of three floating point absorbers located at the grid points of an equilateral triangular, with a solid weight located at the centre of the triangle, which was extended to more complex equilateral triangular grid arrays. The study was based on frequency domain analysis which requires, not only the power take-off system (PTO) to be linear, but also linear mooring forces, which is quite unrealistic as a model of slack moorings. In the present paper those restrictions are removed by using a time-domain, rather than a frequency domain, analysis, which allows nonlinear mooring forces to be considered. The mooring cables are approximately modelled as catenary lines in a quasi-static analysis. The results show very different behaviour for the horizontal and vertical motions of the floating converters, namely the possibility of occurrence of low-frequency horizontal oscillations of large amplitude. Even in the case of incident regular waves, such horizontal motions were found to be non-periodic, a behaviour that is typical of nonlinear systems.