I believe I have solved, at least in principle, the long-standing problem of the Kirkwood gaps, and have incidentally initiated a new approach to questions of orbital stability. I shall begin with the concept I call hyperperiod. A given periodic dynamical system S with period P may or may not have a latent long period - the hyperperiod P∗. If P∗ exists, then any small displacement or variation, actual or virtual, once-for-all or recurrent, will induce a displacement y which will be periodic with period P∗ and will be of bounded amplitudes. We can then say that S is stable. If P∗ dose not exist, then y will eventually become indefinitely large - and we say that S is unstable.