In regular wave groups (bi-chromatic waves) the wave drift forces acting on a tanker consist of a mean wave drift force, an oscillating wave drift force and a wave drift damping force. By means of model tests or 3-dimensional potential theory the quadratic transfer function of the wave drift force and the wave drift damping can be determined. For the low frequency surge motions of a linearly moored tanker exposed to regular wave groups the computational procedure is shown. To validate the computational procedure model tests have been carried out. The computational code is extended to irregular head waves (multichromatic waves) and verified by means of model tests.