The displacement of Newtonian fluids by non-Newtonian fluids in a horizontal cylindrical tube has been investigated both theoretically and experimentally. Theoretical expressions for the breakthrough time, a function of the constitutive constants of the fluids and of the flow parameters and geometry, are derived when the displacing fluids are either of the inelastic viscous or viscoelastic type. The dynamics of the displacement process is studied experimentally using the photometric method and an oil held spacer fluid and glycerol-water mixtures as the displacing and displaced fuids, respectively. The ratio of the zero shear viscosities of the displacing and displaced fluids plays a crucial role when the displacing fluid is characterized either by a viscoelastic or a viscoinelastic structure. The density ratio of the displacing and displaced fluids is close to one in our experiments as it may be in most field operations. We show that characterization of this type of spacer fluid by a viscoelastic model at moderate pressure gradients will not lead to good predictions of the breakthrough time when the:viscosity of the displaced crude is much smaller than that of the displacing spacer fluid, that is, for high values of the zero shear viscosity ratios which may be desirable for high efficiency displacement processes.