Abstract: This study presents a summary review of the basic causes of occurrence and nature of economic cycles. It considers the logistic curve as a valuable function for determination of the basic tendency of time series of economic variables and proposes new approaches to mathematical representation of economic waves. These approaches are based on introduction of the following parameters in the model: asymmetry, period and amplitude of oscillations. The proposed functions allowed to develop a system including seven comprehensive economic models. The study also provides descriptions of the new parameters introduced in the model, i.e. parameters of asymmetry, amplitude and contraction and expansion. Examples of real economic data approximated by the studied mathematical functions are provided. Then, based on the obtained results assertions are made about the consistency of the models and their application both on macro and micro levels.