We propose to generalize Bekenstein model for the time variation of the fin
e structure "constant" cue, to QCD strong coupling constant alpha (S) We fi
nd that, except for a "fine tuned" choice of the free parameters, the exten
sion cannot be performed trivially without being in conflict with experimen
tal constraints and this rules out alpha (S) variability. This is due large
ly to the huge numerical value of the QCD vacuum gluon condensate when comp
ared to the matter density of the universe. (C) 2001 Published by Elsevier
Science B.V.