The peculiarity of offshore cranes, i. e. cranes based on ships or drilling platforms, is not only a significant motion of their base, but also the taut-slack phenomenon. Under some circumstances a rope can temporarily go completely slack, while a moment later, the force in the rope can increase to nominal or even higher value. Periodic occurrence of such phenomena can be damaging to the supporting structure of the crane and its driver. In the paper, mathematical models of offshore cranes that allow for analysis of the taut-slack phenomenon are presented. Results of numerical calculations show that the method of load stabilization proposed by the authors in their earlier works can eliminate this problem.