1 Instituto de Geofisica, UNAM, 04510-C.U., Coyoacan, Mexico, D.F., MEXICO

2 Instituto de Fisica Corpuscular, UV, Dr. Moliner 50, Burjassot, 46100,Valencia, SPAIN

3 UPIICSA, I.P.N., Ciencias Basicas, Te 950, Iztacalco 08400, Mexico,D.F.,MEXICO

Present estimations of proton-proton total cross sections at very high energies are obtained from cosmic rays (> 10¹⁷ eV): by means of some approximations, it is possible to get a value for the proton-proton total cross section from the knowledge of the proton-air cross section at these energies. Besides, total cross sections are measured with present day high energy colliders up to 2 TeV in the center-of-mass (10¹⁵ eV in the lab.): several empirical parametrizations, very successful at low energies, can then be used to extrapolate the measured value and get a reasonable estimation of cross sections at higher energies (10¹⁷ eV). Here we use a phenomenological model to estimate proton-proton total cross sections at cosmic ray energies: on the basis of regression analysis we show that the predictions are highly sensitive to the employed data for extrapolation. When both cross section estimations - from accelerators data and cosmic rays results - are compared, a disagreement is observed, amounting to more than 10%, showing a discrepancy beyond statistical errors: using data at 1.8 TeV our extrapolations are incompatible with most of cosmic ray results in the region around 40 TeV.