Dephosphorization of magnetite fines by flotation in such a way as to minimize the fatty acid coating left on the magnetite surfaces is the principal technical challenge facing the mineral processing division of LKAB, Sweden. Modelling of flotation kinetics enables the influence of chemical and operational variables on apatite flotation from magnetite fines to be predicted. Five typical first-order flotation kinetic models are evaluated by statistical techniques, after an estimation of model parameters by a nonlinear least-squares fitting program, with use of the authors' own results and results taken from the literature. Evaluation of the models is based on two aspects: goodness of fit to the experimental results and suitability to describe the flotation behaviour. The first-order models with a rectangular distribution of floatabilities and with fast and slow floating components (F-S model) gave an excellent fit to the experimental results of apatite flotation when compared with the other models, the latter being superior not only in the goodness of fit to apatite flotation and other mineral flotation results but also in its description of flotation behaviour. The kinetic parameters (percentage recoveries and rate constants of fast and slow floating particles) in the F-S model have a physical significance and can thus be used for qualitative as well as quantitative interpretation of flotation performance. The influence of collector dose can be effectively included in the F-S model by making realistic simplifications and relating the collector dose to the fraction of slow floating particles. The ratio of fast and slow rate constants can be used to describe the selectivity of apatite flotation from magnetite.