The dynamic behaviour and stability of single-phase reacting systems has been investigated thoroughly in the past and design rules for stable operation are available from literature. The dynamic behaviour of gas-liquid processes is considerably more complex and has received relatively little attention. General design rules for stable operation are not available. A rigorous gas-liquid reactor model is used to demonstrate the possible existence of dynamic instability (limit cycles) in gas-liquid processes. The model is also used to demonstrate that the design rules of Vleeschhouwer, Garton and Fortuin, Chemical Engineering Science, 47, 1992, 2547-2552, are restricted to a specific limit case; A new approximate model is presented which after implementation in bifurcation software packages can be used to obtain general applicable design rules for stable operation of ideally stirred gas-liquid reactors. The rigorous reactor model and the approximate design rules cover the whole range from kinetics controlled to mass transfer controlled systems and are powerful tools for designing gas-liquid reactors.