In this paper several models in virus dynamics with and without immune response arediscussed concerning asymptotic behaviour. The case of immobile cells but diffusing viruses andT-cells is included. It is shown that, depending on the value of the basic reproductive number R0of the virus, the corresponding equilibrium is globally asymptotically stable. If R0 < 1 then thevirus-free equilibrium has this property, and in case R0 > 1 there is a unique disease equilibriumwhich takes over this property.
