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Multiple-object tracking (MOT) is a challenging task that requires simultaneous reasoning about location, appearance, and identity of the objects in the scene over time. Our aim in this paper is to move beyond tracking-by-detection approaches, that perform well on datasets where the object classes are known, to class-agnostic tracking that performs well also for unknown object classes.To this end, we make the following three contributions: first, we introduce {\em semantic detector queries} that enable an object to be localized by specifying its approximate position, or its appearance, or both; second, we use these queries within an auto-regressive framework for tracking, and propose a multi-query tracking transformer (\textit{MQT}) model for simultaneous tracking and appearance-based re-identification (reID) based on the transformer architecture with deformable attention. This formulation allows the tracker to operate in a class-agnostic manner, and the model can be trained end-to-end; finally, we demonstrate that \textit{MQT} performs competitively on standard MOT benchmarks, outperforms all baselines on generalised-MOT, and generalises well to a much harder tracking problems such as tracking any object on the TAO dataset.