The article describes a methodology to build instationary models from time series of dynamical systems. We give theoretical arguments for the universality of the models and discuss some of the restrictions and actual problems. As practical test for the method we apply the models to the demanding task of the synthesis of musical and speech signals. It is demonstrated that the models are capable to resynthesize the trained signals. At the present state the envelope and duration of the synthesized signals may be controlled. Intended further developments have been shortly described.