The modeling process of bubbles, using advanced mathematical and econometric techniques, is a young field of research. In this context, significant model misspecification could result from ignoring potential nonlinearities and, hence, it would seem wise to ensure that no terms with explanatory power are neglected. More precisely, the present paper attempts to detect and date non-linear bubble episodes. To do so, we use Neural Networks to capture the neglected non-linearities. Also, we provide a recursive dating procedure for bubble episodes. When using data on stock price-dividend ratio S&P500 (1871.1-2014.6), employing Bayesian techniques, the proposed approach identifies more episodes than other bubble tests in the literature, while the common episodes are, in general, found to have a longer duration, which is evidence of an early warning mechanism (EWM) that could have important policy implications.