Classification in biomedical applications is an important task that predicts or classifies an outcome based on a given set of input variables such as diagnostic tests or the symptoms of a patient. Traditionally the classification algorithms would have to digest a stationary set of historical data in order to train up a decision-tree model and the learned model could then be used for testing new samples. However, a new breed of classification called stream-based classification can handle continuous data streams, which are ever evolving, unbound, and unstructured, for instance--biosignal live feeds. These emerging algorithms can potentially be used for real-time classification over biosignal data streams like EEG and ECG, etc. This paper presents a pioneer effort that studies the feasibility of classification algorithms for analyzing biosignals in the forms of infinite data streams. First, a performance comparison is made between traditional and stream-based classification. The results show that accuracy declines intermittently for traditional classification due to the requirement of model re-learning as new data arrives. Second, we show by a simulation that biosignal data streams can be processed with a satisfactory level of performance in terms of accuracy, memory requirement, and speed, by using a collection of stream-mining algorithms called Optimized Very Fast Decision Trees. The algorithms can effectively serve as a corner-stone technology for real-time classification in future biomedical applications.