The kinetics of intramolecular-contact formation between remote functional groups in peptides with restricted conformational flexibility were examined using designed peptides with variable-length proline bridges. As probes for this motion, free radicals were produced using the •OH-induced oxidation at the C-terminal methionine residue of γ-Glu-(Pro)n-Met peptides (n = 0–3). The progress of the radicals’ motion along the proline bridges was monitored as the radicals underwent reactions along the peptides’ backbones. Of particular interest was the reaction between the sulfur atom located in the side chain of the oxidized Met residue and the unprotonated amino group of the glutamic acid moiety. Interactions between them were probed by the radiation-chemical yields (expressed as G values) of the formation of C-centered, α-aminoalkyl radicals (αN) on the Glu residue. These radicals were monitored directly or via their reaction with p-nitroacetophenone (PNAP) to generate the optically detected PNAP•– radical anions. The yields of these αN radicals were found to be linearly dependent on the number of Pro residues. A constant decrease by 0.09 μM J–1 per spacing Pro residue of the radiation-chemical yields of G(αN) was observed. Previous reports support the conclusion that the αN radicals in these cases would have to result from (S∴N)+-bonded cyclic radical cations that arose as a result from direct contact between the ends of the peptides. Furthermore, by analogy with the rate constants for the formation of intramolecularly (S∴S)+-bonded radical cations in Met-(Pro)n-Met peptides (J. Phys. Chem. B2016, 120, 973227513096), the rate constants for the formation of intramolecularly (S∴N)+-bonded radical cations are activated to the same extent for all of the γ-Glu-(Pro)n-Met peptides. Thus, the continuous decrease of G(αN) with the number of Pro residues (from 0 to 3) suggests that the formation of a contact between the S-atom in the C-terminal Met residue and the N-atom of a deprotonated N-terminal amino group of Glu is controlled in peptides with 0 to 3 Pro residues by the relative diffusion of the S•+ and unoxidized N-atom. The overall rate constants of cyclization to form the (S∴N)-bonded radical cations were estimated to be 3.8 × 106, 1.8 × 106, and 8.1 × 105 s–1 for peptides with n = 0, 1, and 2 Pro residues, respectively. If activation is the same for all of the peptides, then these rate constants are a direct indication for the end-to-end dynamics along the chain.