Fault detection and fault isolation for systems including parametric faults is considered in this paper. By using a linear fractional transformation (LFT) description of parametric fault systems, the systems are transformed into equivalent systems including additive fault signals instead. The theory for systems including additive faults is extended to handle the parametric fault case in the same setting. A number of fundamental problems for parametric fault detection in linear systems is formulated and the corresponding solvability conditions are given.