This paper extends the algorithm previously developed by the authors (Ribeiro et al., Comp. Chem. Engng 19, 333, 1995b) to the simulation of the full trivariate (drop volume, age and solute concentration) unsteady-state behaviour of interacting liquid-liquid dispersions, in continuous or batch stirred vessels. The algorithm uses Coulaloglou and Tavlarides (1977) drop interaction model, but it may easily accommodate any alternative models. Both rigid and oscillating drop mass transfer behaviour have been tested. The procedure enables to simulate in detail all relevant aspects of the dynamics of interacting dispersions in mass transfer conditions, namely the gradual approach to steady-state and the response to pulse and step changes in the main process variables. The algorithm’s speed is high, allowing to envisage its future application in the control of mass transfer contacting equipment, with only modest computer resources.