Electromagnetic devices are often operated under non-linear conditions. Therefore, the current and/or the voltage may not be sinusoidal. This is the case when power electronic sources or loads are applied. Ferromagnetic saturation causes the machine to behave non-linearly as well. Four different FEM algorithms to stimulate and approximate the joint effect of the combined non-linearities mentioned are discussed here. A practical example is used to illustrate and compare the approaches used.