By presenting the work of writers new research shows how real-time recurrent neural networks (RNNs) can be applied to expand the range of traditional signal processing techniques and to help combat the problem of prediction. Analysis of the relationship between RNNs and various nonlinear models and filters, and introduces spatio-temporal architectures together with the concept of modularity and nesting? Checking for stability? And relaxation within RNNs ? Presents an on-line learning algorithms for nonlinear adaptive filters and introduced a new paradigm that utilizes the concept of a priori and a posteriori errors, data adaptive reuse, and normalization ? Studies convergence and stability of on-line learning algorithm based on optimization techniques such as contraction mapping and fixed point iteration Explaining the strategy? For the exploitation of inherent relationships between parameters in RNNs Discussing practical? Issues such as predictability and nonlinearity detecting and includes some practical applications in various fields such as modeling and prediction of air pollutants, the discovery of towing and chaos, ECG signal processing and speech processing Recurrent Neural Networks for Prediction offers a new insight into, architecture and learning algorithm, recurrent neural network stability and, consequently, will have an instant attraction.