Summary: We prove that the existence of Spin-structures on an oriented real vector bundle and the number of them can be obtained in terms of 2-fold coverings of the total space of the SO\((n)\)-principal bundle associated to the vector bundle. Basically we use the theory of covering spaces. We give a few elementary applications making clear that the Spin-bundle associated to a Spin-structure is not sufficient to classify such a structure, as pointed out in [J. Milnor, Enseign. Math., II. Sér. 9, 198–203 (1963; Zbl 0116.40403)].