In marine engineering, the dynamics of fixed offshore structures (for oil and gas production or for wind turbines) are normally found by modelling of the motion by a classical mass-spring damped system. On slender offshore structures, the loading due to waves is normally calculated by applying a force which consists of two parts: a linear “inertia/mass force” and a non-linear “drag force” that is proportional to the square of the velocity of the particles in the wave, multiplied by the direction of the wave particle motion. This is the so-called Morison load model. The loading function can be expanded in a Fourier series, and the drag force contribution exhibits higher order harmonic loading terms, potentially in resonance with the natural frequencies of the system. Currents are implemented as constant velocity terms in the loading function. The paper highlights the motion of structures due to non-linear resonant motion in an offshore environment with high wave intensity. It is shown that “burst”/“ringing” type motions could be triggered by the drag force during resonance situations.