The nonlocal behavior of the electrons in strongly modulated and period-averaged electric fields typical of s- and p-striations in neon glow discharge plasmas is investigated by numerically solving the axially inhomogeneous electron Boltzmann equation. A good agreement between the period lengths measured in the striations and those obtained from the spatially periodic electron relaxation in the period-averaged field of the striations is found confirming the close relation of both phenomena. The s- and p-striations represent the fundamental and first harmonics of the inherent periodic electron relaxation. Furthermore, staring from different boundary conditions the establishment of the velocity distribution function and of selected macroscopic quantities of the electrons into unique periodic states under the action of strongly modulated striation-like fields is investigated. It is shown that the same damping processes that cause in homogeneous fields a relaxation into homogeneous states lead to unique periodic states in strongly modulated fields.