We introduce a new formal computational model designed for studying the information transfer among the generations of offspring–producing machines — so–called autopoietic automata. These can be seen as finite state transducers whose “program” can become a subject of their own processing. An autopoietic automaton can algorithmically generate an offspring controlled by a program which is a modification of its parent’s program. We show that the computational power of lineages of autopoietic automata is equal to that of an interactive nondeterministic Turing machine. We also prove that there exists an autopoietic automaton giving rise to an unlimited evolution, providing suitable inputs are delivered to individual automata. However, the problem of a sustainable evolution, asking for an arbitrary autopoietic automaton and arbitrary inputs whether there is an infinite lineage of its offspring is undecidable.