We present, analyze, and numerically evaluate extended algorithms for detecting changes from an acting stochastic process to a number of possible alternatives. The algorithms are sequential, requiring minimal memory capacity and operational complexity, and they incorporate decision thresholds. The performance of the algorithms is controlled by the selection of the thresholds. An on-line learning algorithm is adapting the thresholds dynamically, to attain pre-specified error performance. Asymptotically, the first algorithmic extension detects the acting process correctly in an expected stopping time sense. In addition, the probability of error induced by a re-initialization algorithmic extension converges asymptotically to zero, when the acting process changes infrequently (with order inversely proportional to the value of the decision thresholds). The presented algorithmic systems are quite powerful and their applications are numerous, ranging from industrial quality control, to identification of changes in patterns, to traffic and performance monitoring in high-speed networks.