Summary: A. Makagon [Stud. Math. 136, No. 1, 71–86 (1999; Zbl 0947.60032); J. Multivariate Anal. 78, No. 1, 1–10 (2001; Zbl 1003.60037)] (for the univariate case) and the first author in [P. Gaşpar, Operator Theory: Advances and Applications 153, 143–156 (2005; Zbl 1062.60036)] (for the operatorial case) treated the problem of periodically correlated processes and operatorial periodically correlated random fields, which w.r.t.the time parameter are not necessarily continuous, but merely square locally summable. On the other hand, the authors have restarted in [D. Gaşpar, P. Gaşpar and N. Grindeanu, “On stationary random distribution fields”, to appear] the study of univariate random distribution fields, which was initiated a long time ago by Gelfand and Itô for the case of one continuous time parameter. It is now our aim, by applying the techniques used in the last mentioned article to continue the work from P. Gaşpar [loc.cit.]in the framework of distributions, i.e., by regarding the field as a distribution instead of a function.