An analysis is presented of the boundary conditions for a steady-state flow reactor with axial diffusion and first-order reaction. Conclusions regarding reactor properties are reached as the result of simultaneous solution of the three differential equations for the reaction section, fore and after sections. Axial diffusion may occur in the latter two sections. The limits of behaviour, represented by a plug-flow reactor without diffusivity, and a fully-stirred reactor, are discussed. Contributions of the diffusivities in the three parts of the system to the course of reaction in space are considered.