We study optically-excited nonlocalities in thin films of doped cadmium oxide. Although these effects are usually weak and hardly observable in the optical response of noble metals, the free-electron nonlocality is significantly increased in doped-cadmium-oside thin films. This increase is due mainly to: (i) low electron scattering rates; and (ii) interband transitions due to valence-band and inner-core electrons that occur far from the epsilon-near-zero frequency. The optical nonlocality manifests itself in the blueshift of the epsilon-near-zero mode, an associated reflectance dip, and the onset of higher-order modes. We model the structure using a generalized hydrodynamic theory that treats the free electrons in the film as a viscoelastic fluid. We demonstrate that both elasticity and viscosity play a significant role in the optical response of the film. The elasticity induces optical resonances associated with the longitudinal pressure modes of the free-electrons fluid, leading to a thickness-dependent permittivity. The viscosity introduces nonlocal damping and additional losses. In our view, this demonstration furthers our understanding of the dynamics of light-matter interactions, and adds a significant stepping stone toward the ability to effectively manipulate linear and nonlinear optical properties at the nanoscale.