This paper uses the quasi arbitrary Lagrangian-Eulerian finite element method (QALE-FEM), based on the fully nonlinear potential theory (FNPT), to numerically investigate the interactions between two floating structures moored in close proximity and oblique monochromic waves with different wave amplitudes, frequencies and incident angles. The main focuses of the study are the motion of the FPSO, the wave run-up and the wave loads. Several cases with different configurations are numerically simulated. For some cases, the fully nonlinear results are compared with linear solutions. The nonlinearities involved in the wave elevation and the wave-induced force are investigated.