The paper presents investigations concerning the stability of spherical flames in a premixed lean hydrogen-air atmosphere and their evolution in case of instabilities. This is done by means of numerical simulations using the thermo-diffusive model with one-step finite rate chemical reaction and radiative heat loss under optically thin conditions. In the first part spherical symmetry is imposed leading to a one-dimensional problem. The results obtained in this way are compared with the asymptotic analysis and the numerical simulations from the literature. In the second part these solutions are employed as initial conditions for fully three-dimensional simulations using a high-resolution pseudo-spectral method. It allows the investigation of the nonlinear transient behavior of spherical flames with respect to three-dimensional perturbations. Different scenarios of their evolution are observed: extinction, spherical growth, and splitting. Also, for the first time, a steady flame ball is computed in a three-dimensional simulation. The different numerical and physical issues are discussed in detail and are related to available experimental observations as well as to theoretical analyses. (C) 2003 The Combustion Institute. All rights reserved.