One of the themes that have been approached more and more within the specialised literature is being represented by economic cycles. The analysis of these is very useful in the long term predictions, in finding solutions for the economic raise and for detecting the economic crisis. At the same time, it is underlined in a lot of scientific and research papers, the importance of the sustainable development in the present and future society. In this paper we intend to bring contributions to the study of the cycles of a sustainable economy and we will analyse it having in mind the purpose of creating the sustainable economy. We will demonstrate the fact that curves that represent graphically all these, are not simple logistics anymore, bi-logistics or multilogistics curves, but curves in plan that are obtained by composing logistics functions with the function of the sustainable development or with the function that shapes the economic component of it mathematically. We will present an interpretation of mathematic models within the frame of the sustainable development.