In this work, from the experimental data we evaluate the first C-moments of the multiplicity distributions recently measured in proton-proton collisions at the LHC and compare them with the predictions of two models: the Kharzeev-Levin model and the Bialas-Praszalowicz model. We divide the data into three sets according to their phase space coverage: I: pT>100 MeV and |η |<0.5 ; II: pT>100 MeV and |η |<2.4 and III: pT>500 MeV and |η |<2.4 . The mean multiplicity grows with the energy according to a power law and the power is different for each set. The Cn moments grow continuously with the energy, slowly in Set I and faster in the other sets. Except for KL in Set II, both models reproduce the main features of the data. The negative binomial parameter k decreases continuously with the energy and there is no sign of change in this behavior.