The positioning of centrosomes, or microtubule-organizing centres, within cells plays a critical part in animal development. Here we show that, in Drosophila embryos undergoing mitosis, the positioning of centrosomes within bipolar spindles and between daughter nuclei is determined by a balance of opposing forces generated by a bipolar kinesin motor, KLP61F, that is directed to microtubule plus ends, and a carboxy-terminal kinesin motor, Ncd, that is directed towards microtubule minus ends. This activity maintains the spacing between separated centrosomes during prometaphase and metaphase, and repositions centrosomes and daughter nuclei during late anaphase and telophase. Surprisingly, we do not observe a function for KLP61F in the initial separation of centrosomes during prophase. Our data indicate that KLP61F and Ncd may function by crosslinking and sliding antiparallel spindle microtubules in relation to one another, allowing KLP61F to push centrosomes apart and Ncd to pull them together.