Push-pull tests at fixed plastic strain amplitude or fixed stress amplitude were run on a TWIP steel, and followed by TEM observations, to analyze its cyclic behavior in relation with the deformation mechanisms. The kinematic and isotropic components of the flow stress were measured throughout the whole cyclic hardening/softening stages, and their evolution with the cumulated plastic strain was compared to those measured in tension. The rise of the internal stress was found responsible for the initial cyclic hardening, but this stress reached at most 50 % of the flow stress, as compared to nearly 70% in tension. Special constitutive equations were identified to capture these evolutions, as well as the transition from hardening to softening. Both components of the flow stress slightly decrease during the softening stage, whose origin is discussed, based on TEM observations at peak stress amplitude, or after softening. The present measurements and TEM observations, combined with those from a previous study of twinning/detwinning kinetics in push-pull on the same steel [29], suggest that under cyclic loading, mechanical twinning cannot be responsible for significant kinematic hardening of intragranular nature (or "dynamic Hall-Petch effect"), but rather contributes to a back stress of intergranular origin.