The purpose of this article is to describe various
conditions on the parameters of pairs of nonhomogeneous
Poisson or pure birth processes under which the corresponding
epoch times or interepoch intervals are stochastically
ordered in various senses. We derive results involving
the usual stochastic order, the multivariate hazard rate
order, the multivariate likelihood ratio order, as well
as the dispersive and the mean residual life orders. A
sample of applications involving generalized Yule processes,
load-sharing models, and minimal repairs in reliability
theory illustrate the usefulness of the new results.