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The notion of stability is present in Freud's work. However, the libido theory model limited its use. Kleinian authors have explored this theme in more depth, describing the risks of the loss of ego stability or defensive systems protecting against chaos and mental turbulence. Dynamic systems theory has interested several psychoanalysts since the 1990s, as it seemed to offer a non-deterministic and non-linear model of the human mind. For some, it has a heuristic value as a metaphor for mental functioning; for others it offers the hope of a real formal modelling of metapsychological theories. The author focuses his attention on the forms of stability described in this theory: simple, periodic and structural. He puts forward the hypothesis of transitions from one type of stability to another in the psychoanalytic process, allowing access to the structural stability of representations that retain self-similarity. The analytic situation must offer an open dynamic system between two poles, maternal and paternal, which constitute the strange attractor necessary for the transition from a form of archaic stability to structural stability. Extracts from a child psychoanalysis are used by way of illustration.