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In this paper compliant multistable tensegrity structures with discrete variable stiffness are investigated. The different stiffness states result from the different prestress states of these structures corresponding to the equilibrium configurations. Three planar tensegrity mechanisms with two stable equilibrium configurations are considered exemplarily. The overall stiffness of these structures is characterized by investigations with regard to their geometric nonlinear static behavior. Dynamical analyses show the possibility of the change between the equilibrium configurations and enable the derivation of suitable actuation strategies.