Non-Abelian plasma instabilities may be responsible for the fast apparent quark-gluon thermalization in relativistic heavy-ion collisions if their exponential growth is not hindered by nonlinearities. We study the real-time evolution of instabilities in an anisotropic non-Abelian plasma with SU(2) and SU(3) gauge groups in the hard-loop approximation. We find exponential growth of non-Abelian plasma instabilities both in the linear and in the strongly nonlinear regime, with only a brief phase of subexponential behavior in between. We present results of numerical simulations using 1 dimensional initial configurations for the soft field and discuss preliminary results obtained using fully 3 dimensional soft field initial conditions.