A method for estimating the domain of attraction of an asymptotically stable equilibrium point of a nonlinear dynamical system and for deriving an upper bound on the time of convergence in the estimated domain is presented. It is based on a set of Lyapunov functions defined on nested regions in the state space. The estimated domain, obtained as the union of a subset of these regions, is based on a local Lyapunov-like condition for the convergence of the solution in each region to its inner boundary. A bound on the time of convergence within the estimated domain is given by the sum of the local bounds. This concept is implemented using a class of regions whose boundaries are described by Fourier series.