The ever-increasing use of artificial intelligence in visual perception tasks for autonomous systems has significantly contributed to advance the research on multiobject tracking, which is a function required in several real-time applications (e.g., autonomous driving, surveillance drones, and robotics) to localize and follow the trajectory of multiple objects moving in front of a camera. Most of current tracking algorithms introduce complex heuristics and reidentification models to improve the tracking accuracy and reduce the number of identification switches, without particular attention to the timing performance, whereas other approaches are aimed at reducing response times by removing the reidentification phase, thus penalizing the tracking accuracy. This work proposes a new approach to multiclass object tracking that allows achieving smaller and more predictable execution times with respect to traditional approaches, without penalizing the tracking performance. The idea is to divide the problem of matching predictions with detections into a number of smaller subproblems by splitting the Hungarian association matrix by class and invoking the second reidentification stage only when strictly necessary, thus applying it to a smaller number of elements. Splitting the matching problem into a number of smaller subproblems also allows parallelizing the Hungarian algorithm, further reducing the execution time in multicore processing platforms. The proposed solution was evaluated in complex urban scenarios with different types of objects (as cars, buses, and motorbikes) and different number of instances, showing the effectiveness of the multiclass approach in reducing execution times without penalizing performance, with respect to state-of-the-art trackers.