  We prove the non-linear stability of a large class of spherically symmetric
equilibrium solutions of both the collisonless Boltzmann equation and of the
Euler equations in MOND. This is the first such stability result that is proven
with mathematical rigour in MOND. While we strive to prove our stability
theorems, we develop new, genuinely Mondian ideas how arising mathematical
difficulties can be solved. At some points it was necessary to restrict our
analysis to spherical symmetry. We discuss every point where this extra
assumption was necessary and outline which efforts must be undertaken to get
along without it in future works. In the end we show on the example of a
polytropic model how our stability result can be applied.
