  In this paper we establish a comparison theorem for stochastic differential
delay equations with jumps. An example is constructed to demonstrate that the
comparison theorem need not hold whenever the diffusion term contains a delay
function although the jump-diffusion coefficient could contain a delay
function. Moreover, another example is established to show that the comparison
theorem is not necessary to be true provided that the jump-diffusion term is
non-increasing with respect to the delay variable.
