The pursuit behaviour of houseflies has been analysed by the evaluation of movie films. On the floor, males, but not females, turn towards passing targets. Males as well as females pursue targets in the air. Male chasing seems to be functionally different from female tracking. Males attack targets in the air from below. They sometimes retract from the target fly after an approach. Thus, a chase may be divided into attacks, periods of pursuit and retreats. Males catch females, but not other males. The pursuer is therefore able to discriminate between the sexes. Close approach or contact with the target fly seems to be necessary to obtain the information. During pursuit both sexes increase the rate of turning. The male but not the female target fly performs evasive translatory reactions to the attacks (figure 4). Females do not catch other flies. They often react with a single turn in the direction of a passing object. They seldom follow the target, which is then normally positioned below the tracking fly. The rotations about the vertical and transverse axis (yaw and pitch) are visually controlled in both sexes. The horizontal and vertical error angle, as well as the horizontal and vertical retinal target velocity, influence the turning behaviour. At least in males, further, hitherto unknown, cues seem to be additionally involved in the control of the rotatory movements. The male control systems operate more precisely than those of the females. Rotations are characterized by steplike changes in angular orientation (`turns') at high angular velocity. Smooth rotations at angular velocities less than about 200 deg s^(-1) seem not to play any role either in males or in females. `Sideways' tracking, most probably mediated by rolling about the long axis, occurred in a single sequence only. A correlation between the translation velocity and the distance between pursuer and target is observed in the pursuit sequences of both sexes. This correlation is interpreted as a by-product of the organization of the flight motor. Therefore, neither males nor females control the translation velocity by the distance to the target. The discussion concentrates on the problems in characterizing the control systems and a comparison with data from optical and electrophysiological measurements. The behavioural differences between hoverflies and houseflies are attributed to the different flight motors.