This paper presents the latest results from calculations of the nonlinear development of instabilities in magneto-plasmadynamic (MPD) thruster flows. Linear instability analysis carried out at the Institut fur Raumfahrtsysteme of the Universitat Stuttgart yielded three basic instabilities for stationary MPD thruster flows: a space charge instability, an acoustic wave instability and an electron drift instability. Nonlinear analysis using the quasi-analytical method (QAM) developed by the authors not only yields these instabilities in the lower orders of the QAM hierarchy but also shows their nonlinear evolution in the higher order development, particularly that of the space charge instability which is actually shown to lead to current chopping. Calculation results for the normalized current density and electric field strength as functions of time for various relative gradients are presented.