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The structural and gas-sensitive properties of <i>n</i>-<i>N</i> SnO₂/κ(ε)-Ga₂O₃:Sn heterostructures were investigated in detail for the first time. The κ(ε)-Ga₂O₃:Sn and SnO₂ films were grown by the halide vapor phase epitaxy and the high-frequency magnetron sputtering, respectively. The gas sensor response and speed of operation of the structures under H₂ exposure exceeded the corresponding values of single κ(ε)-Ga₂O₃:Sn and SnO₂ films within the temperature range of 25–175 °C. Meanwhile, the investigated heterostructures demonstrated a low response to CO, NH₃, and CH₄ gases and a high response to NO₂, even at low concentrations of 100 ppm. The current responses of the SnO₂/κ(ε)-Ga₂O₃:Sn structure to 10⁴ ppm of H₂ and 100 ppm of NO₂ were 30–47 arb. un. and 3.7 arb. un., correspondingly, at a temperature of 125 °C. The increase in the sensitivity of heterostructures at low temperatures is explained by a rise of the electron concentration and a change of a microrelief of the SnO₂ film surface when depositing on κ(ε)-Ga₂O₃:Sn. The SnO₂/κ(ε)-Ga₂O₃:Sn heterostructures, having high gas sensitivity over a wide operating temperature range, can find application in various fields.