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[Display omitted] • A theoretical model is proposed to study the peeling of heterogeneous film. • Nine kinds of peeling processes for heterogeneous film are uncovered. • Two kinds of peeling processes experience two peeling instabilities within one peeling period. • An optimal length fraction of stiff section exists for enhancing adhesive performance. • Better adhesion performance enhancement can be achieved by using more flexible film. Although it has been demonstrated that heterogeneous film can enhance adhesion properties without modifying the interface, there is still a dearth of comprehensive studies in the literature regarding the peeling process of such film and the potential instability that may occur during the peeling process. To address these issues, a peeling model based on the cohesion zone model and Euler-Bernoulli beam equation is proposed in this study. Our analysis revealed four previously unknown peeling behaviors: Firstly, there are nine kinds of peeling processes for heterogeneous film. Only one is stable, static peeling process, while the other eight exhibit instability when the peeling front reaches a certain position. Secondly, instability may occur at the interface from the stiff section to the compliant section of the homogeneous film, as well as at stiff section or compliant section. Moreover, two of these peeling processes experience two instabilities within one peeling period – one at the interface from the stiff section to the compliant section and another at stiff section. Thirdly, an optimal length fraction of the stiff section for enhancing adhesive performance exists and its value is largely determined by the strength of the interface material. Specifically, higher interfacial strength results in smaller values of the optimal length fraction. Finally, the maximum peeling force is positively correlated with the bending stiffness ratio, interfacial strength, interfacial toughness, and period length of heterogeneous film. But it is inversely related to the bending stiffness. These findings are crucial for understanding the peeling behavior of heterogeneous film and strongly adhesive interfaces found in nature, and can be applied to optimize adhesive design and performance in practical engineering applications. [ABSTRACT FROM AUTHOR]