Hysteresis effects do occur usually in polymer field‐effect devices. It has been suggested that trap recharging or mobile ions, or formation/dissociation of bipolarons (BP) in the accumulation layer can cause this effect. Here, at first a literature survey on the hysteresis in field‐effect transistors is given. Then examples of measured hysteresis in field‐effect transistors and in metal‐insulator‐semiconductor (MIS) capacitors are presented. The typical peculiarity is the dependency of the flat band voltage on the sweep direction of the gate voltage. Our recent numerical simulations on the trap recharging mechanism in MIS capacitors are continued and extended to transistors. Energetically distributed traps can lead to hysteresis. But the form of the hysteresis deviates from the observed one and extreme parameter values are needed. Thus it is more likely that trap recharging can modify a hysteresis caused by another mechanism. For discussing the bipolaron mechanism the equilibrium between polarons and doubly charged states of the polymer chains was analyzed anew. With a rate constant for the bipolaron formation determined recently by Salleo and Street relaxation times for formation/dissociation are determined. They indicate that these processes can cause the hysteresis. A further possible mechanism influencing the hysteresis is connected with complexes between polarons, bipolarons and mobile counter ions. The estimated rate constants indicate processes on the time scale of the measurements. Numerical simulations of these processes as well as of the role of mobile ions and their reactions are required for a full description of the hysteresis. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)