Most psychoanalytic models of development and change assume an orderly, sequential and predetermined unfolding of psychological functions and structures. Interferences with orderly unfolding challenge the individual and may lead to pathology. These models derive from a worldview associated with the descriptions of change through linear differential equations, which predict a smooth, orderly world. The study of complex systems and their associated non-linear dynamics predicts a very different kind of world: a world with abrupt changes, discontinuities, idiosyncratic developmental lines, and disproportions between causes and effects. The worldview of non-linear dynamics suggests new possibilities for the psychoanalytic model of change and development, and invites confrontation with the adequacy of many widely accepted models. These new possibilities include discontinuous, sudden and qualitative shifts not only in manifest behavior but also in in-depth psychological functioning.