This paper presents the nonlinear dynamic analysis of a structural system with shape memory alloy members. A new time integration scheme is proposed for solving the differential equation of motion obtained for this system. In the new implicit method, it is assumed that the acceleration varies quadratically within each time step. More terms of Taylor series is used by increasing the order of acceleration which expected to have responses with better accuracy than the classical methods. By adopting the above assumption, a new family of unconditionally stable procedures is obtained. Two dynamic loading cases are considered for the numerical example in which the structure is analyzed with elastoplastic behavior as well as structure enhanced with superelastic shape memory alloy connections. The findings display that nonlinear dynamic analysis conducted on such structures showed to be very efficient and accurate. It is also found that, shape memory alloy permits system to recover the initial configuration at the end of the deformation process. The recovery takes place without any residual strains, while dissipating a considerable amount of energy. (C) 2013 Elsevier Ltd. All rights reserved.