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 Semistar G-GCD domains J. Korean Math. Soc.Published online June 10, 2019 wafa gmiza and Sana hizem faculty of sciences of monastir. Tunisia Abstract : Let $\star$ be a semistar operation on the integral domain $D.$\\ In this paper, we prove that $D$ is G-$\widetilde{\star}$-GCD if and only if $D[X]$ is a G-$\star_1$-GCD domain if and only if the Nagata ring of $D$ with respect to the semistar operation $\widetilde{\star},$ $Na(D, \star_f)$ is G-GCD if and only if $Na(D, \star_f)$ is a GCD domain, where $\star_1$ is the semistar operation on $D[X]$ introduced by G. Picozza \cite{Picozza}. Keywords : semistar operation, star operation, polynomial ring, Nagata ring. MSC numbers : 13F20; 13G05; 13A15; 13E99 Full-Text :