Healthcare is one of the key fields that works quite strongly with advanced analytical techniques for prediction of diseases and risks. Data being the most important asset in recent times, a huge amount of health data is being collected, thanks to the recent advancements of IoT, smart healthcare, etc. But the focal objective lies in making sense of that data and to obtain knowledge, using intelligent analytics. Nonlinear systems find use specifically in this field, working closely with health data. Using advanced methods of machine learning and computational intelligence, nonlinear analysis performs a key role in analyzing the enormous amount of data, aimed at finding important patterns and predicting diseases. Especially in the field of smart healthcare, this chapter explores some aspects of nonlinear systems in predictive analytics, providing a holistic view of the field as well as some examples to illustrate such intelligent systems toward disease prediction.