It is generally accepted that enzymes require internal flexibility, or the activation of anharmonic motions, for catalytic activity. However, in general, the timescales and forms of the functionally important motions coupled to progress along the reaction pathway remain poorly understood. A number of biophysical studies have shown that protein dynamics undergo a temperature-dependent transition from harmonic to anharmonic motion. The purpose of this study was to further investigate the relationship between protein dynamics and catalytic activity, and also to investigate the nature of the observed dynamic transition. The activity and dynamics of the single subunit enzyme xylanase, were measured under similar conditions, from –70 to +10⁰C. The activation of anharmonic picosecond-timescale motions is seen above –50⁰C, whereas the activity was seen to follow Arrhenius behaviour over the entire temperature range investigated. This result suggests that the enzyme rate-limiting step is independent of fast anharmonic motions below –50⁰C. Cryoenzymology studies of the temperature dependence of catalase and alkaline phosphatase activity showed no deviations from Arrhenius behaviour down to temperatures near –100⁰C. These results, as well as earlier studies on glutamate dehydrogenase, indicate that the observed independence of low temperature activity on global anharmonic picosecond­timescale motion may be a general property of both single- and multi-subunit enzymes. Characterisation of cryosolvent properties, such as viscosity and phase changes, by DSC, DMTA, and X-ray scattering techniques, was used to select cryosolvents suitable for low temperature dynamic and activity measurements. A cryosolvent consisting of 70%methanol/10% ethylene glycol/20% water was particularly ideal, as it was the least viscous and free of phase-changes down to at least –160⁰C. The effect of cryosolvents on enzyme properties was investigated, to enable the effect of solvent and temperature on the enzyme to be distinguished. The effect of varying solution composition on the picosecond timescale dynamics of xylanase was investigated by dynamic neutron scattering. The results indicate a significant effect of the solvent, as the picosecond fluctuations of the protein solution largely follow that of the corresponding pure solvent. The results also indicate that the picosecond-timescale atomic motions respond strongly to melting of pure water, but are relatively invariant in cryosolvents of differing compositions and melting points. The temperature dependence of the dynamic transition observed for glutamate dehydrogenase-cryosolvent solutions was also determined. Dynamic neutron scattering experiments were performed with two instruments of different energy resolutions, allowing the separate determination of the average dynamical mean-square displacements on timescales of up to approximately 100 ps and 5 ns. The results showed a significant dependence on the timescale of the temperature profile of the mean-square displacement. The lowest temperature at which anharmonic motion is observed is dependent on the time window of the instrument used to observe the dynamics. These results suggest that the temperature dependence of the dynamic transition in average protein motions is timescale dependent. A possible explanation is that motions over a given timescale are progressively replaced by slower motions, as the temperature is reduced.