The Structural Models, recently suggested by Harvey, uses the classic idea of modelling a time series y its non observed components. The cyclical component of the series, which is defined by a smoothed sine, is a special one that may be used for explaining a repetitive behaviour along the series. The motivation for using this component lies in the finite valued peak presnted by its theoretic spectrum. Harvey´s model stays that the cycle of the series is defined by a single smoothed sine. However, the estimated spectrum of certain series showed that it is reasonable to suppose the cyclical component of those series as being a sum of distinct smoothed sines of different frequencies. This thesis proposses an extension of the cyclical component in Harvey´s model and discusses the equivalent ARIMA structure for this extended component. We develop a Lagrange Multipliers test in the frequence domain for verifying the existence of an extra frequence in the cyclical component. The theory presented in the dissertation is applied with the purpose of testing the presence of a second frequence in the cycle of the series of sunspot numbers and in the series of rainfall in Fotaleza.