This paper is concerned with the identification of static nonlinear components in a complex interconnected system. These nonlinear components are treated nonparametrically, in the sense that no natural parameterization is assumed to be available. A unified framework based on linear fractional transformations for exploring these identification problems is developed. Two key assumptions are made: the linear components of the interconnection are known, and the inputs to all the nonlinear components are available. Under these assumptions, a novel identification algorithm is offered. This algorithm estimates the nonlinear components by minimizing a quadratic cost function. A critical component of this cost function is the inclusion of a dispersion function that captures the requirement that the estimated nonlinearities be static. It is shown that the estimated nonlinearities converge asymptotically to their "true" values under certain identifiability and persistence of excitation conditions. Computable tests for identifiability and sufficient conditions for persistence of excitation are offered. The results in this paper strongly suggest that the most tractable identification problems for nonlinear interconnected systems are those where the inputs to all the nonlinear blocks are measured.