Gas-phase structural modifications induced by the oxidation of methionine of the two peptides of reverse sequence, methionine-valine (Met-Val) and valine-methionine (Val-Met), have been studied by mass-selected IR multiple photon dissociation (IRMPD) spectroscopy in the 800-2000 cm-1 fingerprint range at the Centre Laser Infrarouge d'Orsay free-electron laser facility. The oxidation has been achieved by •OH radicals generated by γ radiolysis. IRMPD spectra were interpreted by static and harmonic DFT calculations and Born-Oppenheimer molecular dynamics simulations, which are employed to take into account all anharmonic and finite-temperature effects. The diagnostic signature of the sulfoxide group in the final products of Met-Val and Val-Met oxidations, which is missing in the spectra of native peptides, has been recorded. Evidence has also been gathered that a mixture of R and S isomers of close energies is formed. An interconversion between different isomers has been unveiled in the case of the oxidized Met-Val dipeptide.