This paper proposes a new space telescope design in which the classical truss structure of the telescope is replaced by a tensegrity structure. A tensegrity structure is a prestressed structure whose structural shape is guaranteed by the interaction between elastic members in tension (tendons) and a set of rigid members (bars). A nonlinear dynamical model of a two stage tensegrity telescope is derived. Static analysis is performed for tensegrity telescopes composed of two stages. The performance specifications for the control system are formulated in terms of the peak value (L∞ norm) of the pointing and alignment errors. The control system is designed to minimize a certain upper bound on this peak value subject to a peak value constraint on the external disturbances. Evaluations of the design are performed through numerical simulations of the closed loop system.