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In this paper, we discuss covering properties in countable products of Čech-scattered spaces and prove the following: (1) If $Y$ is a perfect subparacompact space and $\{X_n:n\in \omega \}$ is a countable collection of subparacompact Čech-scattered spaces, then the product $Y\times {\prod }_{n\in \omega }{X}_n$ is subparacompact and (2) If $\{X_n:n\in \omega \}$ is a countable collection of metacompact Čech-scattered spaces, then the product ${\prod }_{n\in \omega }{X}_n$ is metacompact.