We consider the discrete survival red blood cells model (*) $N_{n+1}-Nₙ=-\delta ₙNₙ+Pₙe^{-a{N}_{n-k}}$, where δₙ and Pₙ are positive sequences. In the autonomous case we show that (*) has a unique positive steady state N*, we establish some sufficient conditions for oscillation of all positive solutions about N*, and when k = 1 we give a sufficient condition for N* to be globally asymptotically stable. In the nonatonomous case, assuming that there exists a positive solution Nₙ*, we present necessary and sufficient conditions for oscillation...