  In this paper, we develop the theory for classifying all the geometric
fibrations of compact, connected, flat $n$-orbifolds, over a 1-orbifold, up to
affine equivalence. We apply our classification theory to classify all the
geometric fibrations of compact, connected, flat $2$-orbifolds, over a
1-orbifold, up to affine equivalence. This paper is an essential part of our
project to give a geometric proof of the classification of all closed flat
4-manifolds.
