  This paper studies the positive solutions of a class of delay differential
equations with two delays. These equations originate from the modeling of
hematopoietic cell populations. We give a sufficient condition on the initial
function for $t\leq 0$ such that the solution is positive for all time $t>0$.
The condition is "optimal". We also discuss the long time behavior of these
positive solutions through a dynamical system on the space of continuous
functions. We give a characteristic description of the $\omega$ limit set of
this dynamical system, which can provide informations about the long time
behavior of positive solutions of the delay differential equation.
