Measurements of cross sections of inelastic and diffractive processes in proton–proton collisions at LHC energies were carried out with the ALICE detector. The fractions of diffractive processes in inelastic collisions were determined from a study of gaps in charged particle pseudorapidity distributions: for single diffraction (diffractive mass M X 3) σ DD/σ INEL=0.11±0.03,0.12±0.05, and 0.12+0.05−0.04 , respectively at s√=0.9,2.76, and 7 TeV . To measure the inelastic cross section, beam properties were determined with van der Meer scans, and, using a simulation of diffraction adjusted to data, the following values were obtained: σINEL=62.8+2.4−4.0(model)±1.2(lumi) mb at s√=2.76 TeV and 73.2+2.0−4.6(model)±2.6(lumi) mb at s√=7 TeV . The single- and double-diffractive cross sections were calculated combining relative rates