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The growth of protocells is discussed under different hypotheses (one or more replicators, linear and nonlinear kinetics) using a class of abstract models (Surface Reaction Models). A method to analyze the dynamics of successive protocell generations is presented, and it is applied to the problem of determining whether the duplication times of the protocell itself and of its genetic material eventually tend to a common value. The importance of the phenomenon of emergent synchronization for sustained protocell population growth and for evolvability is discussed.