The kinetics of enthalpy relaxation (recovery) at the glass transition in xK(2)O.(20-x)MgO.80TeO(2) glasses has been examined from heat capacity measurements using differential scanning calorimetry to clarify the features of the structural relaxation in ternary TeO2-based glasses. Ternary glasses such as 10K(2)O.10MgO.80TeO(2) show high thermal resistance against crystallization compared with binary glasses. The degree of fragility In estimated from the activation energy for viscous flow E-eta and the glass transition temperature T-g is m = 55-62, indicating a fragile character in TeO2-based glasses. Large heat capacity changes of 43.1-48.2 J.mol(-1).K-1 are also observed at the glass transition. The activation energy for enthalpy relaxation Delta H is evaluated from the cooling rate dependence of the limiting fictive temperature, and values of Delta H = 897-1268 kJ.mol(-1) are obtained. Negative deviation from additivity in Delta H is also observed, Values of the Kovacs-Aklonis-Huchinson-Ramos (KAHR) parameter theta estimated front Delta H and T-g are 0.33-0.42 K-1. It has been proposed that ternary glasses have more homogeneous and constrained glass structure compared with binary glasses.