The methods of Brown and Winters are, undoubtedly, the most popular exponential smoothing techniques used nowadays. However, both methods have limitations, such as: Brown s method is applicable only to non-seasonal series and Winters use the linear structure as the only possible model for the trend. A generalization of the smoothing methods in which the limitations cited above are eliminated is presented here. In particular, through a unique analytical formulation, the trend model (constant, linear or quadratic) is linked to the seasonal factors (additive or multiplicative). A forecast error variance estimator is provided and the adaptive control of the non-seasonal part smoothing constant is proposed. A computer program was written for automatic implementation of the method. This program also performs initial values estimation for the process initialization. Some series were generated and processed for testing the method performance. Several suggestions are given for future research which may yield, upon further analysis, to method improvement.