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The threshold currents of a variety of multifilament, composite NbTi superconductors, both twisted and untwisted, have been measured and the results analyzed. The threshold current is defined as a minimum level of transport current which results in a sample quench following a flux jump. The twisted samples are able to maintain much higher levels of threshold current than the untwisted samples. Flux‐jump‐induced quenches existed in all samples, but analysis of the results reveals that different heat‐transfer regimes were operative in the twisted and untwisted materials. For the case of twisted samples, the magnetic energy released in a flux jump is relatively small, and heat transfer is by nucleate boiling; in untwisted samples the energy released is much greater, and heat transfer is by film boiling. The threshold current levels computed for both the twisted and untwisted samples agree satisfactorily with the experimental results.