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The recent experimental synthesis of the monolayer γ -GeSe, characterized by its unique Mexican-hat band dispersion, has attracted considerable research interest. However, the exploration of band gap engineering in bilayer γ -GeSe and γ -SnSe through the application of strain and electric fields remains under-investigated. In this study, we demonstrate that both strain and electric fields are effective methods for band gap engineering in bilayer γ -GeSe and γ -SnSe. We have discovered that strain can not only tune the band gap but also induce a transition from an indirect to a direct band gap. Furthermore, it is observed that the band gap of bilayer γ -GeSe and γ -SnSe can be modulated by an electric field, potentially leading to a transition from semiconductor to metal. Our findings suggest that band gap engineering via strain and electric fields is a promising approach for designing nanoelectronic and optoelectronic devices based on bilayer γ -GeSe and γ -SnSe.