In this paper, we continue the construction of the time-optimal control problems classification for nonlinear affine analytic systems in a neighborhood of the equilibrium. The moment approach is the basis of this investigation. All possible asymptotics for solutions of the nonlinear time-optimal control problems are described in terms of special right ideals in the algebra of nonlinear power moments. We demonstrate the possible asymptotic behavior of the time-optimal control for a certain class of essentially nonlinear three-dimensional systems.