In this article the authors propose a modality of prognosis of the quantities of waste generated in a certain period. The proposal was finalized by achieving a model of prognosis by using dynamic systems based neural networks for the time series prediction. Time series with three components were used: trend, seasonality and residual variable. According to the input data, one can choose the adjustment model regarding the description of the phenomenon analyzed (additive and multiplying). In this scope the Cascade_Correlation algorithm was used, a constructive learning algorithm. Starting from the input data a time series generates, with 1, 2 or  3 ahead (according to how we want to make the prognosis: for a month, for two months or for three months ahead). The advantages of the algorithm are the more rapid convergence and the elimination of the necessity to determine a priori the topology of the network. In the study the Quickpropagation learning algorithm was presented, used in order to involve the output units and candidate from the Cascade_Correlation algorithm. In the article a case study is presented for the analysis of data and for the time series prediction by using the soft made in Matlab and Neurosheel program. A comparison between the input data and those prognosticated by the neural network was made.