Abstract The formation of “horns” on diffusion paths in two-phase diffusion couples having a common matrix phase is analyzed by considering the one-dimensional form of the diffusion equation. It is shown that horns occur when flux versus distance profiles have a finite slope at the initial diffusion couple interface. In particular, the equations predict that only single horns will form, even though double horns have been reported in the literature. A model ternary system is used as an example. The model system illustrates that when the effective diffusivity is constant, the diffusion path follows a linear zigzag course and has no horns. Also, the flux profiles are symmetric with a peak at the initial interface. However, when the effective diffusivity is modeled to vary with composition, the peak shifts away from the initial interface and the flux profile has a finite slope at the origin. The result is a diffusion path with a single horn, in agreement with theory.