Description: Usual treatments of multiple-decrement theory are on a nonselect basis, with all rates of decrement depending only on attained age. This paper develops the theory on a select basis, carried out fully in the stochastic framework. The relationship between select periods in a multiple-decrement model and those of the associated single-decrement models is investigated. A discussion of the paper follows. From Transactions of Society of Actuaries 1991, Vol. 43.