The present paper is concerned with some aspects of stability and of steady periodical changes in dynamical systems. After a brief survey of the classical theory due to Poincaré, I shall sum up some of my recent work relating to a certain class of systems not considered in that theory. It is, of course, assumed that this work is relevant to the main subject of this meeting; in fact, in the course of writing down these notes I was fortunate enough to be able to look (although far too cursorily) through Dr. Ashby's book, Design for a Brain, and have been struck by what appeared to me to be a remarkable parallelism between our lines of thought. The arrangement of the subject-matter has been avowedly influenced by this assumption of relevancy; however, I shall keep to my legitimate grounds as a physicist and shall leave it to you to fill in what ever “psychological” conclusions you may think justified.