The problem of the possibility of the existence of a special nonlinear effect arising in the marine environment, called “rouge waves”, is considered. Rouge waves are a phenomenon that cannot be described by means of the apparatus of linear wave theory, the existence of which is beyond doubt. There are various hypotheses explaining the occurrence of rouge waves, but there is no generally accepted point of view about the nature of their occurrence. The paper presents a formal apparatus that generalizes the concept of a dynamic system, in which it is possible to formulate the necessary conditions imposed on the system that determine the occurrence of a rouge wave.