Hadron inclusive spectra in pp collisions are analyzed within the modified quark-gluon string model including both the longitudinal and transverse motion of quarks in the proton in the wide region of initial energies. The self-consistent analysis shows that the experimental data on the inclusive spectra of light hadrons like pions and kaons at ISR energies can be satisfactorily described at transverse momenta not larger than 1-2 GeV/c. We discuss some difficulties to apply this model at energies above the ISR and suggest to include the distribution of gluons in the proton unintegrated over the internal transverse momentum. It leads to an increase in the inclusive spectra of hadrons and allows us to extend the satisfactory description of the data in the central rapidity region at energies higher than ISR.
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