Starting from the Glansdorff and Prigogine method established to study the stability of thermodynamic systems, and following the Lyapunov analysis, the expression of a functional that is able to find the stability limits of fluids with internal structure is given. Making use of this functional, one derives the thermodynamic and hydrodynamic criteria of stability for micropolar fluids. As applications the Helmholtz-Korteweg theorem for the slow motion of Newtonian fluids is generalised to the micropolar case and the influence of the microrotations in the Rayleigh-Benard problem is outlined. © 1981, Walter de Gruyter. All rights reserved.