It has long been our view that Liapunov’s direct method is the leading technique for dealing with stability problems in many areas of differential equations. We have contributed to that theory for more than forty years and continue to do so. Yet, numerous difficulties with the theory and application to specific problems persist and it does seem that new methods are needed to address those difficulties. There is, of course, the problem of constructing appropriate Liapunov functionals and in carrying out various calculations such as is seen in the annulus argument. These are things which we feel we can overcome with work and imagination.