Self-excited induction generators produce power off-grid with capacitors placed in parallel with the load to supply the reactive power. The existing theory predicts an exponential growth of the phase voltages from the zero state when the linearized electrical system has unstable poles, a condition that requires a combination of minimum speed and sufficient capacitance. In practice, however, pre-charged capacitors are often used to ensure self-excitation, a precaution that the linear theory does not predict a need for, since any nonzero initial condition, no matter how small, should trigger exponential growth towards self-excitation. Instead, experiments reported in the paper show a clear relationship between successful self-excitation and the voltage initially applied to the capacitors. In some cases, growth of the voltages is also found to be significantly slower than exponential. Further, instances are found where sinusoidal voltages are sustained for many cycles before collapsing. None of these behaviors fit the linear theory. An explanation of the experimental data is proposed in the paper, assuming a nonlinear dependency of the magnetizing inductance on the magnetizing current for low values of the current, in addition to the magnetic saturation at high currents. A model of the induction generator that accounts for these effects is proposed, and simulations show that the characteristics of the experimental responses can be duplicated.