Second-order rate constants ($k_N$) have been measured spectrophotometrically for $S_NAr$ reactions of Y-substituted-phenoxy-2,4-dinitrobenzenes (1a-1g) with hydrazine and glycylglycine in 80 mol % $H_2O$/20 mol % DMSO at $25.0{pm}0.1^{circ}C$. Hydrazine is 14.6-23.4 times more reactive than glycylglycine. The magnitude of the ${alpha}$-effect increases linearly as the substituent Y becomes a stronger electron-withdrawing group (EWG). The Br${o}$nsted-type plots for the reactions with hydrazine and glycylglycine are linear with ${eta}_{lg}=-0.21$ and -0.14, respectively, which is typical for reactions reported previously to proceed through a stepwise mechanism with expulsion of the leaving group occurring after rate-determining step (RDS). The Hammett plots correlated with ${sigma}^{circ}$ constants result in much better linear correlations than ${sigma}^-$ constants, indicating that expulsion of the leaving group is not advanced in the transition state (TS). The reaction of 1a-1g with hydrazine has been proposed to proceed through a five-membered cyclic intermediate ($T_{III}$), which is structurally not possible for the reaction with glycylglycine. Stabilization of the intermediate $T_{III}$ through intramolecular H-bonding interaction has been suggested as an origin of the ${alpha}$-effect exhibited by hydrazine.