M. A. Nowak and C. R. M. Bangham, 1996 developed three ordinary differential equations models for infection dynamics. The model which we studied consists of four variables i.e. uninfected cells, infected cells, free virus particles and virus specific CTLs. We discussed the stability of the equilibrium points to predict long time behaviour of the system. We proved that global stability of the equilibria having only uninfected cell and for other equilibria we investigated conditions under which equilibrium points will be asymptotically stable. Then we introduced time delay in the model and studied conditions under which steady states will be asymptotically stable. We examined that for endemically infected equilibrium a critical value of time delay may occur. The steady state may be asymptotically stable when delay will be less than critical value and when delay passes through critical value then uninfected cells, infected cells, free virus and CTLs may undergo cyclic oscillations.