Summary: Seiberg-Witten equations which are formed by Dirac equation and curvature-equation, have some generalizations on 8-dimensional manifold [A. H. Bilge et al., Commun. Math. Phys. 203, No. 1, 21–30 (1999; Zbl 0946.58028); N. Özdemir and N. Değirmenci, J. Dyn. Syst. Geom. Theor. 7, No. 1, 21–39 (2009; Zbl 1187.53049); Y.-h. Gao and G. Tian, J. High Energy Phys. 2000, No. 5, Paper No. 036, 22 p. (2000; Zbl 0990.81550)]. In this paper we consider the Spin\(^c\)-structure which was given in [Bilge et al., loc. cit.]. Then by using this Spin\(^c\)-structure, we examine the curvature equations which were given in [Bilge et al., loc. cit.; Özdemir and Değirmenci, loc. cit.]. Finally we show the equivalence between them.