This paper describes the development of a tilting locomotion system based on a compliant tensegrity structure with multiple stable equilibrium configurations. A tensegrity structure featuring 4 stable equilibrium states is considered. The mechanical model of the structure is presented and the according equations of motion are derived. The variation of the length of selected structural members allows to influence the prestress state and the corresponding shape of the tensegrity structure. Based on bifurcation analyses a reliable actuation strategy to control the current equilibrium state is designed. In this work, the tensegrity structure is assumed to be in contact with a horizontal plane due to gravity. The derived actuation strategy is utilized to generate tilting locomotion by successively changing the equilibrium state. Numerical simulations are evaluated considering the locomotion characteristics. In order to validate this theoretical approach a prototype is developed. Experiments regarding to the equilibrium configurations, the actuation strategy and the locomotion characteristics are evaluated using image processing tools and motion capturing. The results verify the theoretical data and confirm the working principle of the investigated tilting locomotion system. This approach represents a feasible actuation strategy to realize a reliable tilting locomotion utilizing the multistability of compliant tensegrity structures.