One of the most interesting applications of superconductors in power systems is the so called “Superconductor Fault Current Limiter (SFCL)”. This is a device that makes the lines exhibit a variable short-circuit impedance: very low (almost null) under normal operation, and high when the current increases above the security limit of the line. There are two types of SFCL: resistive and inductive. The first one consists of a superconducting element in series with the line. The element is designed with a critical current equal the security limit of the line. When the current in the line is higher, the element transits and a high resistance arises, protecting the line. The second type is connected in series with the line too. It consists of an inductor with the magnetic core shielded by a superconducting screen. The screen is designed to transit by magnetic field when the current in the coil (line current) is higher than the security limit of the line. At this time, a high reactance arises protecting the line. The PhD thesis we are working on is a new concept of SFCL with two stages (resistive and inductive) in series designed to solve some problems of each type separately. In this case, the resistive stage is located in the gap of the inductive stage magnetic core. Firstly, the objective is to make the magnetic screen transit. When this happens, the magnetic field penetrates the core and surrounds the resistive stage provoking its transition. In this paper, we present the work philosophy of this novel device, which does not have equivalent in conventional (non-superconducting) technology.