Abstract 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.