The dynamical evolution of microstructure in the two-phase region of peritectic system is examined in which the nucleation of the new phase and the relative growth rates of the nuclei and the parent phase need to be considered for the final selection of the microstructure. Critical experimental studies have been carried out which show that in large diameter samples, i.e. diameter > 3.0 mm, convection effect in the melt is dominant, and it gives rise to a novel microstructure which consists of a large tree-like domain of primary a-phase that is embedded inside the peritectic b-phase. A new experimental technique is developed in which samples of different diameters, ranging from 0.2 mm to 6.0 mm, can be directionally soslidified simultaneously to examine the effect of convection. In hyperperitec alloys, the tree-like structure observed in large diameter sample disappears when the sample diameter is reduced to 0.6 mm, and a single a to b transition is observed, as predicted by the diffusive model. In the hypoperitectic composition, as predicted by the diffusive model, discrete is observed in thin samples of 0.6 mm diameter. This is the first evidence of diffusive bands which are controlled by the repeated nucleation of the two phases in which banding cycle opoerates below and above the peritectic temperature. When the sample size is reduced, several new dynamical structures have been observed in the diffusive regime. A detailed dynamical model in the diffusive regime is developed, using the phase.field approach, which explains the observed morphologies, and shows that the selection of a particular morphology is governed by the relative growth rates of the nuclei and the parent phase. The effect of convection on microstructure development is examined through a detailed numerical model of convection. The effects of steady-state and oscillatory convection have been examined. It is shown that oscillatory convection, present in large diameter samples, can give rise to a tree-like structure that is observed experimentally.