This paper focuses on the characterization of delay effects on the asymptotic stability of some continuous-time delay systems encountered in modeling the post-transplantation dynamics of the immune response to chronic myelogenous leukemia. More explicitly, we shall discuss the stability of the crossing boundaries of the corresponding linearized models in the delay-parameter space. Weak, and strong cell interactions are discussed, and analytic characterizations are proposed. An illustrative example completes the presentation.