We present an algorithm for simultaneously inverting an unknown cylindrically stratified permittivity and conductivity profile. The algorithm is based on a recently developed inversion method referred to as the renormalized source type integral equation approach. This method provides an explicit dependence on the unknowns to be inverted for and hence allows one to compute the derivatives of the fields with respect to these unknowns (the Jacobian and Hessian matrices) in an explicit form. Furthermore, by prestoring the entries of the inversion equation, which depend only on the background medium and are independent of the unknown profile, the method reported here does not require solving the full forward problem repeatedly as in the case of the distorted Born approach and is therefore faster in implementation. ¿ American Geophysical Union 1994