The complex dynamics of a simple two-compartment model of the production and regulation of circulating blood neutrophil number are investigated.It is addressed that the possibility of the proliferative disorders may be due to both the factors of the apoptosis rate (r)S of the haematopoietic stem cell and the cell cycle duration TS.Using the developed geometrical criterion for the Hopf bifurcation and transient behavior of the delay systems to this model, we separate the stable regime from unstable regime in the (r)S-TS plane.The patterned periodic oscillation regimes with low periodicity in the number of circulating blood cells are illustrated in the (r)S-TS plane.As the value of TS above its critical level is increased, the transitions from period-1 to period-5 by adding period bifurcation and eventually to complex strange attractors are found.As the value of (r)S above its critical level is increased, however, the simple period-adding bifurcation phenomena occur which eventually lead to periodic solutions with large periodicity.