  The different forms of propagation of relativistic electron plasma
wavepackets in terms of Airy functions are studied. It is shown that exact
solutions can be constructed showing accelerated propagations along coordinates
transverse to the thermal speed cone coordinate. Similarly, Airy propagation is
a solution for relativistic electron plasma waves in the paraxial
approximation. This regime is considered in time-domain, when paraxial
approximation is considered for frequency, and in space-domain, when paraxial
approximation is considered for wavelength. In both different cases, the
wavepackets remains structured in the transverse plane. Using these solutions
we are able to define generalized and arbitrary Airy wavepackets for electron
plasma waves, depeding on arbitrary spectral functions. Examples of this
construction are presented. These electron plasma Airy wavepackets are the most
general solutions of this kind.
