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Various MgB2 wires with different sheath materials provided by Hyper Tech Research Inc., have been tested in the superconducting fault current limiter (SFCL) desktop tester at 24–26 K in a self-field. Samples 1 and 2 are similarly fabricated monofilamentary MgB2 wires with a sheath of CuNi, except that sample 2 is doped with SiC and Mg addition. Sample 3 is a CuNi sheathed multifilamentary wire with Cu stabilization and Mg addition. All the samples with Nb barriers have the same diameter of 0.83 mm and superconducting fractions ranging from 15% to 27% of the total cross section. They were heat-treated at temperatures of 700 °C for a hold time of 20–40 min. Current limiting properties of MgB2 wires subjected to pulse overcurrents have been experimentally investigated in an AC environment in the self-field at 50 Hz. The quench currents extracted from the pulse measurements were in a range of 200–328 A for different samples, corresponding to an average engineering critical current density (Je) of around 4.8 × 104 A cm−2 at 25 K in the self-field, based on the 1 µV cm−1 criterion. This work is intended to compare the quench behaviour in the Nb-barrier monofilamentary and multifilamentary MgB2 wires with CuNi and Cu/CuNi sheaths. The experimental results can be applied to the design of fault current limiter applications based on MgB2 wires.