[en] A mathematical model of the pulsed coil system of a tokamak which treats the plasma loop as a coil, too, is presented. The parameters involving this 'plasma coil' may vary with time. Both the equations describing the dynamics of the complete coil system and the formulae for calculating all system parameters are collected. On this basis two concrete pulsed coil models are set up: PCOILS 1 is a simple model, mainly for the purpose of quickly calculating the most relevant voltages, currents, and energies. PCOILS 2 is a more involved model, mainly for studying control problems such as position and burn control. The numerical solution of the sets of equations representing PCOILS 1 and PCOILS 2, and the continuous checking of the energy balance of the system during the solution is described. In connection with PCOILS 2 the passive stabilization of the plasma position by chamber wall currents is treated in terms of the mutual inductance of the plasma loop and dipole chamber currents. Finally, the PCOILS 1 and PCOILS 2 models are applied to the current rise phase of the ASDEX divertor tokamak and to the compression phase of the ZEPHYR tokamak ignition experiment. (orig.) 891 GG/orig. 892 HIS