Reactions among particulate solid phases are important and abundant in many materials, chemical, and metallurgical process industries. Many of these are reaction networks, and not single-step reactions as normally assumed. There is no theoretical framework available for the analysis of such systems, and single-reaction models derived from the gas-solid literature continue to be used. Formation of cement clinker in the rotary cement kiln is a prime example of the genre, in which mechanistic aspects play an important role in determining energy efficiency and the composition and nature of the phases that form. In the present study, we formulate a model within the ambit of the "shrinking core" class of models, for reactions in series among solid phases. The model shows the presence of one or two moving fronts in the reacting particle, depending on the relative rates of the processes involved. A single Thiele-type parameter controls the model behavior, at once describing the relative rates of the intermediate formation and consumption processes, and the diffusion-reaction competition for the product formation step. The model has been shown to reduce to the well known single reaction models at the limits of low and high values of the Thiele parameter. Experimental data have been obtained on the calcia-alumina system, an important one it? cement manufacture, in the temperature range 1150-1250 degrees C. The model has been fitted to these data and the kinetic parameters determined. The comparison bears out the salient features of the theory, and shows that a degree of diffusion limitation exists for the intermediate conversion step under these conditions. The diffusivity values estimated are in the range of 10(-19) to 10(-18) m(2)/s and agree with values found in the literature for similar systems. The rate constant for the intermediate conversion step is of the order of 10(-6) s(-1). This being among the first such determinations, this value awaits confirmation from other studies. (C) 2009 American Institute of Chemical Engineers AIChE J, 55: 2399-2413, 2009