During anaphase identical sister chromatids separate and move towards opposite poles of the mitotic spindle. In the spindle, kinetochore microtubules have their plus ends embedded in the kinetochore and their minus ends at the spindle pole. Two models have been proposed to account for the movement of chromatids during anaphase. In the 'Pac-Man' model, kinetochores induce the depolymerization of kinetochore microtubules at their plus ends, which allows chromatids to move towards the pole by 'chewing up' microtubule tracks. In the 'poleward flux' model, kinetochores anchor kinetochore microtubules and chromatids are pulled towards the poles through the depolymerization of kinetochore microtubules at the minus ends. Here, we show that two functionally distinct microtubule-destabilizing KinI kinesin enzymes (so named because they possess a kinesin-like ATPase domain positioned internally within the polypeptide) are responsible for normal chromatid-to-pole motion in Drosophila. One of them, KLP59C, is required to depolymerize kinetochore microtubules at their kinetochore-associated plus ends, thereby contributing to chromatid motility through a Pac-Man-based mechanism. The other, KLP10A, is required to depolymerize microtubules at their pole-associated minus ends, thereby moving chromatids by means of poleward flux.