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This study gives the temperature dependence of the Raman bandwidths for the $\nu 5(174cm-1)$ mode of $NH4Cl$ and for the $\nu 5(177cm-1)$ mode of $NH4Br$. We analyze our observed Raman bandwidths of those phonon modes according to the soft-hard mode coupled model close to the phase transitions in these crystals. Our analyses give that the values of the critical exponent for the Raman bandwidths are $\beta =0.13$ for the $\nu 5(174cm-1)$ mode of $NH4Cl(Tc=241.3K)$ and for the $\nu 5=(177cm-1)$ mode of $NH4Br(Tc=234K)$ in the first order phase region of these crystalline systems.