Various rod-shaped bacteria mysteriously glide on surfaces in the absence of appendages such as flagella or pili. In the deltaproteobacterium Myxococcus xanthus, a putative gliding motility machinery (the Agl-Glt complex) localizes to so-called focal adhesion sites (FASs) that form stationary contact points with the underlying surface. Here we show that the Agl-Glt machinery contains an inner-membrane motor complex that moves intracellularly along a right-handed helical path; when the machinery becomes stationary at FASs, the motor complex powers a left-handed rotation of the cell around its long axis. At FASs, force transmission requires cyclic interactions between the molecular motor and the adhesion proteins of the outer membrane via a periplasmic interaction platform, which presumably involves contractile activity of motor components and possible interactions with peptidoglycan. Our results provide a molecular model of bacterial gliding motility.