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Generalized pseudostandard words were introduced by de Luca and De Luca in 2006. In comparison to the palindromic and pseudopalindromic closure, only little is known about the generalized pseudopalindromic closure and the associated generalized pseudostandard words. In this paper we provide a necessary and sufficient condition for their periodicity over a binary and a ternary alphabet. More precisely, we describe how the directive bi-sequence of a generalized pseudostandard word has to lookdoi:10.37236/4771 fatcat:lnpix5vjpfbaleftsr5uwktaky