In this article, the linear viscoelastic properties of a family of metallocene-catalysed ethylene homopolymers and ethylene/1-hexene copolymers near the 'plateau' and in the terminal regions have been measured. The zero shear viscosity and relaxation time both scale to 3.41 power of the molecular weight, as is observed for most of the linear polymers. At the same time, no theological signs associated with the presence of long chain branching are detected. However, an unexpected low value of the plateau modulus has been found. This result is discussed in terms of a possible decrease in the entanglement density and/or an increase in chain flexibility with respect to other model polymers. A simple method, previously tested in the literature, based on simplified molecular dynamics, enables a correct description of the dynamic modulus from the knowledge of the form of the molecular weight distribution and the material theological constants G(N)(o) and eta (o)