The solid-state reaction kinetics of a sequential reaction system were analysed theoretically and experimentally. For the reactions occurring in series, A+R --> B and B+Q --> C, a multiple core-shell diffusion-controlled model has been proposed. The relations between the consumption fractions of A and B and the reaction time under isothermal conditions have been quantitatively deduced. The sequential reactions of PbWO4+PbO --> Pb2WO5 and Pb2WO5MgO+MgO --> Pb(Mg1/2W1/2)O-3 in the formation processes of Pb(Mg1/2W1/2)O-3 were utilized as the model reactions. The unidirectional diffusion of PbO into PbWO4 to form Pb2WO5 and that of MgO into Pb2WO5 to generate Pb(Mg1/2W1/2)O-3 were verified by EDS. The derived equations were confirmed to elucidate accurately the kinetics of the serial reactions in the Pb(Mg1/2W1/2)O-3 system. Based on the reaction model, the activation energy for the diffusion of MgO into Pb(Mg1/2W1/2)O-3 was estimated to be 161.7 kJ mol(-1).