A solution is presented for electron plasma oscillations in a thermalized plasma, at arbitrary ratios of the Debye length AλD and the perturbation wavelength λ. The limit λD≪λ corresponds to the conventional fluid-like theory of small particle excursions, whereas λD≫λ corresponds to the free-streaming limit of strong kinetic phase mixing due to large particle excursions. A strong large-Debye-distance (LDD) effect already appears when λD ≳ λ. The initial amplitude of the fluid-like contribution to the macroscopic density perturbation then becomes small compared with the contribution from the free-streaming part. As a consequence, only a small fraction of the density perturbation remains after a limited number of kinetic damping times of the free-streaming part. The present analysis can be considered as a first exercise in an attempt to tackle the far more difficult problem of large-Larmor-radius (LLR) effects in a magnetized plasma. The analysis further shows that a representation in terms of normal modes of the form exp (— iωt) leads to amplitude factors of these modes that are related to each other and that depend on the combined free-streaming and fluid behaviour of the plasma. Consequently, these modes are coupled and cannot be treated as independent of each other.