Stimuli-responsive flexible metal-organic frameworks (MOFs) remain at the forefront of porous materials research due to their enormous potential for various technological applications. Here, we introduce the concept of frustrated flexibility in MOFs, which arises from an incompatibility of intra-framework dispersion forces with the geometrical constraints of the inorganic building units. Controlled by appropriate linker functionalization with dispersion energy donating alkoxy groups, this approach results in a series of MOFs exhibiting a new type of guest- and temperature-responsive structural flexibility characterized by reversible loss and recovery of crystalline order under full retention of framework connectivity and topology. The stimuli-dependent phase change of the frustrated MOFs involves non-correlated deformations of their inorganic building unit, as probed by a combination of global and local structure techniques together with computer simulations. Frustrated flexibility may be a common phenomenon in MOF structures, which are commonly regarded as rigid, and thus may be of crucial importance for the performance of these materials in various applications.