Microtubule-based ATPases of the kinesin superfamily provide the motile force for many animated features of living cells. Kinesin motors differ in their direction of movement along microtubules. Kinesin and ncd, a kinesin-related motor involved in formation and maintenance of mitotic and meiotic spindles, move in opposite directions along microtubules, even though their motor domains are 40% identical in amino-acid sequence. Here we report the crystal structure of the MgADP complex of the Drosophila ncd motor domain determined to 2.5A by X-ray crystallography, and compare it to the kinesin structure. The ncd and kinesin motor domains are remarkably similar in structure, and the locations of conserved surface amino acids suggest these motors share a common microtubule-binding site. Moreover, structural and functional comparisons of ncd, kinesin, myosin and G proteins indicate that these NTPases may have a similar strategy of changing conformation between NTP and NDP states. We propose a general model for converting a common gamma-phosphate-sensing mechanism into opposite polarities of movement for kinesin and ncd.