Attention is focused on the interdiffusional aspects of the diffusional bonding problem as it relates to the fabrication of clad fuel elements and their operation at elevated temperatures. Certain idealized cases of core-cladding interdiffusion occurring in single phase, two-phase, and three-phase systems are examined analytically. In the two-phase and three-phase systems, the importance of the roles played by the boundary and interface concentrations and the diffusion coefficients in controlling interface movement and interdiffusion is evaluated in detail.