The use of intelligent systems for stock market prediction has been widely established. In this paper, we investigate how the seemingly chaotic behavior of stock markets could be well represented using several connectionist paradigms and soft computing techniques. To demonstrate the different techniques, we consider the Nasdaq-100 index of Nasdaq Stock MarketSM and the S&P CNX NIFTY stock index. We analyze 7-year Nasdaq 100 main-index values and 4-year NIFTY index values. This chapter investigates the development of novel, reliable, and efficient techniques to model the seemingly chaotic behavior of stock markets. We consider the flexible neural tree algorithm, a wavelet neural network, local linear wavelet neural network, and finally a feed-forward artificial neural network. The particle-swarm-optimization algorithm optimizes the parameters of the different techniques. This paper briefly explains how the different learning paradigms could be formulated using various methods and then investigates whether they can provide the required level of performance — in other words, whether they are sufficiently good and robust so as to provide a reliable forecast model for stock market indices. Experiment results reveal that all the models considered could represent the stock indices behavior very accurately.