A general kinetic model of the process of formation of amyloid protofibrils is suggested, which allows calculation of the size of the protofibril nuclei using only kinetic data.This model includes the stage of primary nucleation, the linear growth of protofibrils (proceeding only at the cost of attaching of monomers to their ends) and a possible exponential growth of protofibrils at the cost of either growth from the surface, or fragmentation, or branching with the secondary nuclei.Theoretically, only the exponential growth is compatible with the existence of a pronounced lag-period (which can take much more time than the growth of aggregates themselves).The obtained analytical solution allows us to determine the size of the primary and secondary nuclei from the experimentally obtained concentration dependences of the time of growth and of the ratio of the lag-time duration to the time of growth of amyloid protofibrils.The theoretical results are used to analyze the experimental data taken from literature and our own experiments.