The work in this Letter is aimed at propossing some ideas on the definition of the fragility as a function of thermodynamic parameters for a reduced set of OG-formers: cycloheptanol, cyclooctanol and their binary mixtures. Previous possible proposals such as Delta C-p, or (Delta T-g1/T-g1(A)) are now reexamined. Among other proposals, (Delta C-p/C-p,C-g1) can correlate with (Delta T-g1/T-g1(A)) such that a link between the thermodynamic (Delta C-p/C-p,C-g1) relation and kinetic (F-1/2)-parameters can be outlined. Data either from the literature or measured by us of certain glass-forming materials have been used to extend this link to a more general approach. In addition, an alternative proposal in which the volume is considered as a thermodynamic variable is also discussed. (C) 2007 Elsevier B.V. All rights reserved.