A method of analytic continuation is advanced for computing ac responses of electrochemical systems with arbitrary electrode geometries and proposed as an exact alternative to the approximate and intuitive transmission line models (TLMs). Using a complex extension of the boundary element method, the small signal ac responses were computed for several Hull cell geometries, the rectangular pore, the saw-tooth and a fractal geometry. A comparison with the results of the TLMs for the rectangular pore and the saw-tooth reveal quantitative as well as qualitative differences. Besides providing a bench-mark for such approximate theories, the present method may well be the only option for system geometries not amenable to a TLM. An alternative approach to the study of the constant phase element based on analytic continuation is also sketched. (c) 2007 Elsevier B.V. All rights reserved.