The deformation properties of composites (CM) with shape memory alloy (SMA) fibers and a linearly elastic binder are significantly limited by small deformations of the binder. One of the ways to overcome this disadvantage is the use of viscoelastic binders with limited creep and deformations reversible after unloading over time, the magnitude of which is comparable to the deformations of SMA returned during the reverse phase transformation. CM with shape memory alloy elements and viscoelastic binder exhibit rheonomic (i.e. time-scale-dependent) behavior. Therefore, the analysis of the influence of the rate of temperature change of fibers on the functional properties of such CM is an urgent task. The article describes the results of solving such a problem for unidirectional CM in the framework of the model of nonlinear deformation of SMA during phase and structural transformations and the model of a standard linear body for a viscoelastic binder. Special attention is paid to the study of the influence of the rate of temperature change and the viscoelastic properties of the binder on the possibility of implementing a closed two way shape memory effect in CM. It is established that when the rate of temperature change of SMA fibers tends to infinity, the behavior of CM with a viscoelastic binder tends to the behavior of the same composite, but with an elastic binder if the instantaneous modulus of the viscoelastic binder is equal to the Young’s module of the elastic binder. At the same time, when the rate of temperature change tends to zero, the behavior of KM with a viscoelastic binder tends to the behavior of KM with an elastic binder, the Young’s modulus of which is equal to the long-term modulus of the viscoelastic binder. A method is proposed for determining the filling coefficient that ensures the implementation of a closed two way shape memory effect in KM with a viscoelastic binder by solving the problem for the case of an elastic binder.