Agarose hydrogels are used to study the tribological response of hydrogel materials. We demonstrate that the dynamic frictional behaviour of agarose hydrogels is influenced by their mechanical properties, lubricant viscosity and applied load. Within the linear viscoelastic regime of the hydrogels, we find the Stribeck-type framework proposed previously for elastomers and other viscoelastic materials describes their tribological behaviour and dependency on lubricant viscosity. However, this breaks down when sufficient stress in the contact is applied so that the hydrogel undergoes yielding (i.e. elastic-plastic deformation). As a result, we find that the friction- normal load relationship differs from the classic trend (F ~ W2/3) observed in elastomers above finite loads. Conventional interpretations of the friction associated with hydrogels should be revised with consideration for the non-linear deformation of the hydrogels. We suggest that theories on viscoelastic lubrication are generally applicable to hydrogels within their linear viscoelastic regime, and propose a conceptual model that considers the effects of bulk mechanical properties and measurement conditions including lubricant viscosity, measuring geometry, speed and load.