This paper suggests and compares two approaches for building a fuzzy-rule based system for time series modeling and forecasting. The first one is based on a constructive offline learning (C-FSM). The second one, is based on an adaptive online learning process (A-FSM). Both models have its general architecture based on a fuzzy rule based system, and its respective learning algorithms are based on the EM optimization technique. Because the C-FSM is trained in an offline learning, it results in a more accurate model. However, the A-FSM has a faster learning process, since it is not necessary to retrain it with all data available at each iteration. The A-FSM also provides a more compact structure, being its learning and structure generation, great advantages in terms of time process and computational effort, when compared to the constructive approach. Results applying both techniques for building time series models show their efficiency, having each one of them important advantages when compared. The constructive offline model gets better accuracy, but, the online one, has a faster learning and a provides a simpler final structure. © 2007 IEEE.