The shear moduli and viscosities of monolayers of two polymers, poly(methyl methacrylate) (PMMA) and poly(vinyl stearate) (PVS), and of two simple amphiphiles, octadecanol and behenic acid, were measured at various stages of compression. Monolayers of the simple amphiphiles exhibited low values of these viscoelastic properties, with the shear moduli being below 0.2 mN m-1 and the viscosities below 0.25 mN s m-2. Changes with increasing surface pressure appear to correlate with changes in monolayer phase. The viscoelastic properties of the polymer monolayers were found to have much higher values than those of the simple amphiphiles : for PMMA, the values of shear modulus and viscosity were up to 20 mN m-1 and 700 mN s m-1, respectively; for PVS, up to 100 mN m-1 and 5000 mN s m-1, respectively. With PMMA the viscoelastic properties showed a dependence on molar mass when compared on an area basis but little dependence when compared at the same surface pressures. There was a clear correlation between the shear viscoelasticity of the monolayers and the development of surface pressure gradients during compression.