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Coal and gas outburst is a type of coal mine dynamic disaster with complex causes and serious consequences. In China, the number and scale of outburst disasters are among the highest in the world. It is an inevitable stage for outburst that the mechanical instability of the combination of intact coal and tectonic coal (CICTC) in strata. The dip angle of the interface has an important influence on the instability of CICTC-containing gas. To further understand the instability process of CICTC, the uncoordinated deformation of CICTC was defined. According to this, three strain conditions were delimited. The variations of stress under three strain conditions were analyzed, the expressions of additional interfacial stress were established. Then, based on the Mohr–Coulomb criterion, the strength characteristics and failure forms were analyzed. It was found that the dip angle deflects the principal stress in the interface, and the influences of additional stresses on the value of principal stress are opposite. These two reasons make the principal stress state and instability process of the combination complicated. Finally, combined with actual parameters, the instability processes of CICTC under different stress paths and buried depths were studied. It can be found that the failures of CICTC under different stress paths were concentrated appearing in the tectonic coal body, intact coal interface, and tectonic coal interface. With the increase of buried depth, the initial maximum principal stress increases and the reduction from additional stresses to the strength of intact coal interface enhances, which makes the combination damage easily and the failure form change. The research results in this paper can provide a theoretical basis to prevent and control the outburst of the combination containing gas considering the dip angle of the interface. Highlights: The uncoordinated deformation of combination considering the dip angle was first defined. The expressions of additional interfacial stress of combination considering the dip angle were established The influences of different stress paths and buried depths for the instability of combination were discussed quantificationally. [ABSTRACT FROM AUTHOR]