  The concept of stability, originally introduced for polynomials, will be
extended to apply to the class of entire functions. This generalization will be
called Hurwitz stablility and the class of Hurwitz stable functions will serve
as the main focus of this paper. A first theorem will show how, given a
function of either of the Stieltjes classes, a Hurwitz stable function might be
constructed. A second approach to constructing Hurwitz stable functions, based
on using additional functions from the Laguerre-P\'{o}lya class, will be
presented in a second theorem.
