The present paper is concerned with the derivation of the electric and magnetic surface currents induced on a cylindrically curved impedance strip. By considering the locality of the high-frequency diffraction phenomena the physical (-pi,pi) interval for the usual cylindrical polar angle is replaced by an abstract infinite interval (-infinity,infinity) whereby the related mixed boundary value problem is formulated as a ''modified matrix Hilbert'' problem. By using the Debye approximations for the Hankel and Bessel functions involved, the modified matrix Hilbert problem is first decoupled and then reduced to two pairs of simultaneous Fredholm integral equations of the second kind which are solved by iterations. The explicit expressions for the electric and magnetic surface current components attributable to the reflection, edge or surface diffractions of the incident field as well as to the edge reflections of these components themselves are obtained by evaluating the current integrals asymptotically. The results derived in this paper constitute also a rigorous proof for a conjecture made by Idemen on the reflections of the surface currents at the edges.