Summary: The stability of core-annular flows is of fundamental scientific and practical importance. The interface between two immiscible fluids can become unstable by several physical mechanisms. Surface tension is one of those mechanisms of practical importance. We include in our model the effects of insoluble surfactants. The full problem is derived considering the surfactant transport equation. We carry out an asymptotic solution of the problem when the annulus is thin compared to the core-fluid radius and for waves which are of the order of the pipe radius. We obtain from matched asymptotic analysis a system of two coupled nonlinear partial differential equations for the interfacial amplitude and the surfactant concentration on the interface.