The significant increase in the available computational power that took place in recent decades has been accompanied by a growing interest in the application of the evolutionary approach to the synthesis of many kinds of systems and, in particular, to the synthesis of systems like analog electronic circuits, neural networks, and, more generally, autonomous systems, for which no satisfying systematic and general design methodology has been found to date. Despite some interesting results in the evolutionary synthesis of these kinds of systems, the endowment of an artificial evolutionary process with the potential for an appreciable increase of complexity of the systems thus generated appears still an open issue. In this thesis the problem of the evolutionary growth of complexity is addressed taking as starting point the insights contained in the published material reporting the unfinished work done in the late 1940s and early 1950s by John von Neumann on the theory of self-reproducing automata. The evolutionary complexity-growth conditions suggested in that work are complemented here with a series of auxiliary conditions inspired by what has been discovered since then relatively to the structure of biological systems, with a particular emphasis on the workings of genetic regulatory networks seen as the most elementary, full-fledged level of organization of existing living organisms. In this perspective, the first chapter is devoted to the formulation of the problem of the evolutionary growth of complexity, going from the description of von Neumann's complexity-growth conditions to the specification of a set of auxiliary complexity-growth conditions derived from the analysis of the operation of genetic regulatory networks. This leads to the definition of a particular structure for the kind of systems that will be evolved and to the specification of the genetic representation for them. A system with the required structure — for which the name analog network is suggested — corresponds to a collection of devices whose terminals are connected by links characterized by a scalar value of interaction strength. One of the specificities of the evolutionary system defined in this thesis is the way these values of interaction strength are determined. This is done by associating with each device terminal of the evolving analog network a sequence of characters extracted from the sequences that constitute the genome representing the network, and by defining a map from pairs of sequences of characters to values of interaction strength. Whereas the first chapter gives general prescriptions for the definition of an evolutionary system endowed with the desired complexity-growth potential, the second chapter is devoted to the specification of all the details of an actual implementation of those prescriptions. In this chapter the structure of the genome and of the corresponding genetic operators are defined. A technique for the genetic encoding of the devices constituting the analog network is described, along with a way to implement the map that specifies the interaction between the devices of the evolved system, and between them and the devices constituting the external environment of the evolved system. The proposed implementation of the interaction map is based on the local alignment of sequences of characters. It is shown how the parameters defining the local alignment can be chosen, and what strategies can be adopted to prevent the proliferation of unwanted interactions. The third chapter is devoted to the application of the evolutionary system defined in the second chapter to problems aimed at assessing the suitability in an evolutionary context of the local alignment technique and to problems aimed at assessing the evolutionary potential of the complete evolutionary system when applied to the synthesis of analog networks. Finally, the fourth chapter briefly considers some further questions that are relevant to the proposed approach but could not be addressed in the context of this thesis. A series of appendixes is devoted to some complementary issues: the definition of a measure of diversity for an evolutionary population employing the genetic description introduced in this thesis; the choice of the quantizer for the values of interaction strength between the devices constituting the evolved analog network; the modifications required to use the analog electronic circuit simulator SPICE as a simulation engine for an evolutionary or an optimization process.