A 5-axis turning-milling complex center (TMC) is regarded as the combination of a turning center (TC) and a machining center (MC). However, in structural kinematic chains and kinematic properties, TMCs are pretty different from TCs and MCs, which causes that TMC error generations has inherent properties. This paper researched kinematic chain, controllable axis, simultaneous moving axis, processable part face and error component, from the view of machine structures. A simple calculation formula of error component numbers on CNC machine tools is pointed out according to controllable axis numbers. Through setting up space kinematic equation on TMC, translational and rotational axis error influences are considered. Some views are put out on the error measurement, identification, modeling and compensation for the future research.