An asymmetry in ionospheric conductivity between two hemispheres results in the formation of additional, interhemispheric field-aligned currents (FACs) flowing between conjugate ionospheres within two auroral zones. These interhemispheric currents are especially significant during summer-winter conditions when there is a significant asymmetry in ionospheric conductivity in two hemispheres. In such conditions, these currents may be comparable in magnitude with the Region 1 (R1) field-aligned currents. In this case, the R1 current is the sum of two FACs: one is going from/to the solar wind, and another is flowing between conjugate ionospheres. These interhemispheric currents can also cause the formation of auroras extended along the nightside polar cap boundary, which may be related to the so-called "double auroral oval." In this study, we present the results of analytical and numerical solutions for the interhemispheric currents and their effect on the Region 1 currents.