  Kummer's Conjecture predicts the rate of growth of the relative class numbers
of cyclotomic fields of prime conductor. We extend Kummer's Conjecture to
cyclotomic fields of conductor n, where n is any natural number. We show that
the Elliott-Halberstam Conjecture implies that this Generalised Kummer's
Conjecture is true for almost all n but is false for infinitely many n.
