We investigate nonlocal electrodynamics based on the generalized hydrodynamic approach including electron diffusion in holey gold films, showing extraordinary optical transmission (EOT). Dramatic changes with respect to the local approximation for rather large film thicknesses t less than or similar to 100 nm impact both reflectance and absorbance at normal incidence. Beyond the familiar resonance blueshift with the decreasing film thickness, the interference of longitudinal pressure waves in the holey structure generates an unexpected oscillatory response with geometrical parameters. An increase in the transmittance relative to the local result of up to 33% (typically up to +/- 6% at resonance) was observed, but it can also be suppressed when absorption dominates. We expect that our findings will stimulate additional studies of EOT when taking into consideration nonlocal effects in holey films of experimentally accessible parameters in two-dimensional hole arrays. Published by AIP Publishing.