Differential equations are developed for the normal propagation of plane electromagnetic waves in an isotropic, plane stratified, inhomogeneous gyrational medium for which D = εE + ξH, B = ζE + μH. Energy considerations are required to determine the necessary boundary conditions at infinity, and the reflection properties of two lossless models are discussed, these being the semi-infinite slab and the model with continuous exponential variation of properties. Both the independent circularly polarized waves and the dependent linearly polarized waves are considered. © 1969 Oxford University Press.