  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 binary and
ternary alphabet. More precisely, we describe how the directive bi-sequence of
a generalized pseudostandard word has to look like in order to correspond to a
periodic word. We state moreover a conjecture concerning a necessary and
sufficient condition for periodicity over any alphabet.
