Unidirectional solidification for the peritectic Sn-1.0, 1.5, 2.0 at% Cd alloys was carried out under temperature gradients of 2.7 x 10(3) K/m for 4 mm diameter specimens, and 5.3 x 10(3) K/m for 2 mm diameter specimens. A banded structure in which the two constituent phases alternatively form perpendicular to the growth direction was observed in the 2 mm diameter specimens. On the other hand, a competitive microstructure was obtained in the 4 mm diameter specimens, in which the two phases interlace and the three-phase junction fluctuated in the radial direction during unidirectional solidification. Formation of the banded structure depended on the specimen diameter, while the transition from the cellular interface to the planar interface was not affected by the specimen diameter. In the high G/V region for peritectic alloys, the growth morphology in which the phases grow side by side is unstable, even if the pulling rate and temperature profile are constant. The banded structure and the competitive structure originate through the same mechanism; this is intrinsic for peritectic alloys with two-phase composition.