We analyze the mathematical structure of a multicomponent reactive mixture in a plug flow reactor with axial diffusion. Quasilinearity of the kinetic equation assuming "uniformity" does not carry over to the second-order equations when diffusion is considered and a perturbation expansion method needs to be developed. Perturbation around the limit of a CSTR is regular, which leads to nonhomogeneous second-order differential equations containing no unknown kinetic term, so that the procedure cascades down to the solution of the CSTR problem. Perturbation around the PFR problem is singular, but the inner (boundary layer) solution is easy. The outer solution leads to a series of integro-differential equations, which can be reduced to complete Volterra integral equations of the second kind, these are known to admit unique solutions. A formal approach to finding these solutions is discussed.