A nonlinear system with distributed delays is studied. The model takes into account the fast self-renewal dynamics observed in Acute Myeloid Leukemia (AML). In this case, stability and instability conditions are derived for the zero equilibrium of the model. Notice that, biologically, the zero equilibrium means the eradication of all malignant cells which is the aim of the anti-AML therapy. The novelty of this work is that we consider time-varying biological parameters reflecting the fact that the differentiating and self-renewing parameters become time-variant both under the effect of the desease and the drugs. A simpler case of the studied model describes the normal process of hematopoiesis. In the latter case we focus on the stability of the strictly positive equilibrium point since it reflects the surviving of all the generations of blood cells. Via a construction of a novel Lyapunov-Krasovskii functional, we derive sufficient conditions for the local exponential stability of the studied equilibrium and we propose an estimate of its basin of attraction.