The composition region for stable coupled peritectic growth is evaluated by means of extending Boettinger's analysis. Our present analysis demonstrates that there exists a critical composition between C-alpha (composition of primary a at peritectic equilibrium) and Cp (compostion of peritectic beta at peritectic equilibrium), i.e. C-crit, separating the peritectic plateau (between C-alpha and C-beta) into two regions where coupled and banded growth regimes dominate between C-crit and C-beta and between C-alpha and C-crit, respectively. The calculated critical composition, C-crit, is consistent with the observation in Ni-Al, Ti-Al and Sn-Cd peritectic systems. Effects of interfacial energies of constituent phases and convection on the separation of these two growth regimes are also discussed.