The main aim of this fellowship is to finish the manuscript of a monograph EVOLUTIONARY STABILITY AND DYNAMICS OF POPULATION SYSTEMS co-authored with József Garay. The authors pursue two main objectives. First, they deal with the problem of synthesis of the following three classical basic models of theoretical biology: Fisher’s selection model, the evolutionary game-theoretical model and the Lotka-Volterra model of interaction of several species. This objective is reached by the extension of the concept of evolutionary stability in several steps. The evolutionary stability concepts to be introduced are partly based on the following Darwinian principle: a population state is evolutionarily stable if rare mutants in this population cannot propagate. In the synthesis of Fisher’s model and evolutionary games, the asymptotic behaviour of processes resulting from different biological situations will be characterized in terms of concepts derived from the static form of the above principle. The results achieved using mathematical tools, may be applied to answer certain questions of evolutionary biology such as when the terminal states of the selection process will coincide in sexual and asexual populations. As for the several-species evolutionary games, the conceptual approach is primarily dynamic, and the long-term evolutionary success of the mutants will depend on the dynamic characteristics of the system describing the interaction. Apart from the coevolutionary context the obtained results can also be applied in ecology, when the behaviour of individuals also depend on the behavior of other individuals of the same species. Important examples are foraging and habitat selection. The other major objective is the investigation of the above-mentioned dynamic models with the tools of mathematical systems theory. The controllability and observability analysis of multi-species models may contribute to the respective methodological development of conservation biology and ecological monitoring systems. Starting from the dynamics of different selection processes, control-theoretical models of artificial selection can be obtained. Based on a selection dynamics, in terms of mathematical systems theory the question can be answered whether observing the time-variation of the phenotypic composition of a population, the underlying genetic process can be recovered.