It is well known that a principle of uniform seniority applies to mortality tables which follow Gompertz's or Makeham's law, and, in a modified form, in the case of certain other laws, such as Makeham's second law and the double geometric law. It is natural to inquire what is the most general class of mortality laws to which such a principle applies. In its most general form the uniform seniority principle implies that the value of a joint-life annuity on m lives of different ages is equal to that of a joint-life annuity (possibly computed at a different interest rate) on k lives of equal age, in such a way that the new interest rate i′, the number of substituted lives k, and the difference between the youngest age and the substituted equal age, depend only on the various differences in age between the youngest life and the other original lives, and not on the actual age of the youngest life.