We study the behaviour in viscoelastic fluids of the high-frequency viscosity factorC(n(ωm)). This factor depends upon the numbern(ωm) of exponential decay terms needed to describe the observed relaxation behaviour in a frequency range 0 to ωm. Quite generallyn(ωm) increases with increasing ωmand decreasing temperature (T).Ccan be interpreted as the ratio η(0)fast/η(0) where η(0) is the zero frequency viscosity, and η(0)fastis that component of the viscosity that is associated with rapidly decaying relaxation processes, i.e. with processes that decay in times shorter than ωm-1. AsTdecreases, more relaxation processes become slow thereby accounting for a decrease inC; at sufficiently lowT, the only fast processes are the very fast (molecular) ones that vary little withTand are called the ‘bare processes’. Thus at lowT,Cis small and varies as η-1. At highT, 1 —Ccan be associated with the shear-orientation parameterR, and at lowTthe quantityCη(0)k2/ρ can be associated with thek-dependent part of the shear wave relaxation frequency.