Measurements of cross sections of inelastic and diffractive processes in proton–proton collisions at LHC en- ergies were carried out with the ALICE detector. The frac- tions of diffractive processes in inelastic collisions were de- termined from a study of gaps in charged particle pseudora- pidity distributions: for single diffraction (diffractive mass MX < 200 GeV/c2) σSD/σINEL = 0.21 ± 0.03, 0.20+0.07, −0.08 and 0.20+0.04, respectively at centre-of-mass energies √s = −0.07 0.9, 2.76, and 7 TeV; for double diffraction (for a pseudora- pidity gap η > 3) σDD /σINEL = 0.11 ± 0.03, 0.12 ± 0.05, and 0.12+0.05 , respectively at √s = 0.9, 2.76, and 7 TeV . To −0.04 measure the inelastic cross section, beam properties were determined with van der Meer scans, and, using a simu- lation of diffraction adjusted to data, the following values were obtained: σINEL = 62.8+2.4(model) ± 1.2(lumi) mb at √ −4.0 s = 2.76 TeV and 73.2+2.0(model) ± 2.6(lumi) mb at √ −4.6 s = 7 TeV. The single- and double-diffractive cross sec- tions were calculated combining relative rates of diffrac- tion with inelastic cross sections. The results are compared to previous measurements at proton–antiproton and proton– proton colliders at lower energies, to measurements by other experiments at the LHC, and to theoretical models.