In devices with flexible displays, multilayer adhesive stacks may be included. A multilayer adhesive may attach a flexible display panel to the display cover layer in an electronic device. Including multiple layers of adhesive in the adhesive stack (as opposed to a single layer) provides more degrees of freedom for the tuning and optimization of the properties of the adhesive stack. The multilayer adhesive stack therefore has better performance than if only a single layer of adhesive is used. The multilayer adhesive stack may include one or more layers of soft adhesive, hard adhesive, hard elastomer, hard polymer, and/or glass to optimize the mechanical and optical performance of the multilayer adhesive stack. Soft adhesive layers may be included to optimize lateral decoupling (e.g., during folding and unfolding) of the adhesive stack. Harder layers may be included to provide rigidity and prevent denting during impact events.