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The ideas of systemic intelligence provide a set of methodologies and paradigms that are, beside other advantages, suitable for constructing control systems that are capable of growing up. In particular the promising methods of systemic architecture, schedule of structural development, memory organization and rules for learning and adaptation are presented and discussed with respect to grow up an artifact. Of special interest is the concept of growth in the sense of growing up from a kind of infantile stage to a fully matured entity. To grow up an artifact from an infantile stage via a sequence of learned abilities to,a fully matured entity is still a feature of life not yet sufficiently transposed onto technical systems. To enable the capability to grow up artifacts, a set of methodologies and principles is presented in this paper. The developed methodologies are already implemented into physically existing test beds that operate, adapt (and grow up) in real time and in the real world to prove that the proposed approach is feasible under real conditions. Two realizations (robot control, audio signal processing) of a systemic architecture for an up-growing system are presented in this paper.