We have used quantum mechanical chemical calculations (CCSD(T)-F12a/cc-pVDZ-F12//M06-2X/aug-cc-pVTZ) to investigate the hydrogen shift (H-shift) reactions in acyl peroxy and hydroperoxy acyl peroxy radicals. We have focused on the H-shift reactions from a hydroperoxy group (OOH) (1,X-OOH H-shift with X = 6, 7, 8, or 9) in the hydroperoxy acyl peroxy radicals, this H-shift is a reversible reaction and it scrambles between two peroxides, hydroperoxy acyl peroxy and peroxy peroxoic acid radicals. The forward reaction rate constants of the 1,X-OOH H-shift reactions are estimated to be above 10(3) s(-1) with transition state theory corrected with Eckart quantum tunnelling correction. The ratio between the forward and reverse reaction rate constant of the 1,X-OOH H-shift reactions is around similar to 10(5). Therefore, the equilibrium is pushed toward the production of peroxy peroxoic acid radicals. These very fast 1,X-OOH H-shift reactions are much faster than the reactions with NO and HO2 under most atmospheric conditions and must be included in the atmospheric models when hydroperoxy acyl peroxy radicals are oxidized. Finally, we have observed that H-shift reactions in a pentane acyl peroxy radical (C5-AOO) is fast (>1 s(-1)); this can have a significant influence on the possible formation of large acyl peroxy nitrate molecules.