Flame-balls are stationary spherical premixed flames observed in certain near-limit mixtures. Sufficiently large flame-balls are subject to a three-dimensional instability which defines a maximum mixture strength for which steady flame-balls can exist. The researchers studied the dynamics of flame- balls in the neighborhood of the neutral stability point and show that there is a transcritical bifurcation and the dynamics is governed by a fifth-order system of nonlinear ordinary differential equations. The late time behavior of the solution of these equations corresponds either to a stationary sphere (stable solution) or a growing prolate spheroid. Prolate spheroids are observed experimentally, and the relationship between the experimental observations and the theoretical predictions.