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The aim of this paper is to compare the properties of cores designed for medium voltage current transformers. The cores were made of SiFe, NiFe polycrystalline strips, and nanocrystalline strips. The properties of cores combined of two different soft magnetic materials, i.e., grain-oriented electrical steel SiFe and NiFe polycrystalline strip (SiFe+NiFe) or grain-oriented electrical steel and Fe-based nanocrystalline strip (SiFe+Nano) also have been determined. The content of harmonic distortions in a magnetizing current in various combinations of toroidal cores is presented. The lowest harmonic distortions occur in cores with grain-oriented electrical steel SiFe and the largest - in cores with NiFe polycrystalline strips among all the tested magnetic circuits. Taking into consideration magnetic properties, the best solution is the SiFe+Nano combined cores this is because of the content of harmonic distortions in comparison to SiFe+NiFe and high values of relative magnetic permeability and the shape of the magnetization curve supporting the use of SiFe+Nano in instrument transformers.