  The event-by-event p_T-fluctuations in proton-proton and central Pb-Pb
collisions, which have been experimentally studied by means of the so-called
Phi-measure, are analyzed. The contribution due to the correlation which
couples the average p_T to the event multiplicity is computed. The correlation
appears to be far too weak to explain the preliminary experimental value of Phi
(p_T) in p-p interactions. The significance of the result is discussed.
