The article reveals the basic principles of the processual approach to the study of personality, which have a natural scientific foundation and are based on the ideas of the philosophy of instability of I. Prigogine. The developed processual approach is designed to overcome the opposition of variability and stability of personality, and to explain how the personality remains sustainable, being in constant change. This question, formulated by Mischel, continues to be debated in modern theoretical and methodological studies, maintaining the controversy between supporters of structural and dynamic paradigms of personality research. The significant role of the theory of non-equilibrium systems for understanding personality changeability is revealed in connection with explanation of its processual nature, when the leading role is played not by the variety of elements and their dynamics, but by self-organization of personality components. The processuality of personality determines its ability to move to new levels of functioning, to become more complex, to unpredictably change structurally and meaningfully in an infinite variety of options. The processual nature of personality focuses attention of a researcher on the potentially possible, when the object of research is not the existing, but the emerging. The methodological principles for describing the processual nature of personality are the principle of contextuality, revealing the sensitivity of its subsystems to fluctuations, the principle of multiplicity (uncertainty) of states, explaining the growth of non-adaptive forms and variability in critical situations and turning points, the principle of historicity, defining events as a starting point of imbalance and consistency, the principles of complementarity and wholeness, describing the dialectic of sustainability and changeability at different levels of functioning (three contexts of personality existence: situational, life and existential).