Tensegrity structures are networks of tensile and compressive truss members that have pre-stressability and shape-morphing capabilities. Potential applications of tensegrities in the aerospace, civil, and robotics fields require them to have actuation capabilities and adjustable stiffness. An approach to infuse these properties into tensegrities is to employ active materials. Shape memory alloys (SMAs) are active materials with the ability of exchanging mechanical and thermal energies. They have actuation capabilities enabled by the shape memory effect and large recoverable deformations enabled by the pseudoelastic effect. This paper presents a study on the integration of actuator and pseudoelastic SMAs into tensegrities to create a new class of stifftruss structures that exhibit controlled large deformations. A model for tensegrities that incorporates mechanical equilibrium, thermal equilibrium, and an SMA constitutive model is first developed. The tensile members in the tensegrities may be comprised of actuator or pseudoelastic SMA wires. The actuator wires can be manipulated through Joule heating to change the shape of the tensegrity structure on demand. The pseudoelastic wires provide high stiffness under moderate external disturbances, and become compliant and allow for large deformations as their stress is increased by the actuator wires. This unique combination of actuator and pseudoelastic SMA members in tensegrities is demonstrated through examples of controlled morphing of a tensegrity beam and a tensegrity plate. The results show that using pseudoelastic members antagonistic to the actuators, as opposed to elastic members, reduces the accumulated error and the energy required to control the tensegrities.