Brillouin light scattering has been used to determine the high-frequency complex mechanical modulus of alkali berate liquids and glasses, as a function of the temperature. The temperature dependence of the complex modulus can be described by an enhanced Maxwell model for linear viscoelastic systems. Accordingly, the module comprises relaxational components and a temperature dependent static modulus, which is determined by the equilibrium volume fraction of kinetically arrested domains. Application of this model to the Brillouin data indicates that the structural relaxations in undercooled glass forming liquids occur via relatively distinct mechanisms, each one becoming thermally activated within a different temperature range. The rate of degradation of the network structure increases with increasing alkali content, and is commensurate of the fragility of the liquid. The structural features which are subject to a change in the context of a particular degradation mechanism are released sequentially, i.e., relaxation, facilitated by the rupture of a given network link, is required before other links of the same type become affected by thermal motion. Mechanisms that are activated at high temperatures involve the diffusional displacements of various atomic species. Immediately above T-g, however, structural relaxations are characterized by the dominance of the bulk viscosity over the shear viscosity, and by positive values of the imaginary part of the complex poison ratio. This indicates that, to a significant degree, compressive deformations and head-on collisions between structural moieties are involved in the structural relaxations at these low temperatures. It is surmised that the deformation of boroxol rings, where a boron moves out of the BO3 plane to exchange one of its oxygen neighbors, is underlying to this relaxation mechanism, which results in an increase of the average network ring size.