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We have analysed the momentum spectra of the secondary particles in p-
p interactions predicted by different models, comparing them with acce
lerator data from 19.7 GeV to 1.8 TeV (CMS). All models predicting asy
mptotic behaviour of secondary spectra with Feynman scaling in the fra
gmentation region lead to a rather slow increase of multiplicity in co
ntradiction to the accelerator data. It is shown that the pure phenome
nological model, which is based on the semi-inclusive spectra from ISR
and FNAL collider experiments at 19.7 GeV, and extrapolated to higher
energies by assuming violated Feynman scaling in the entire phase spa
ce, describes the data well in the whole accelerator range. This model
is also relevant for application in the study of cosmic rays at high
energies.