  Generalized pseudostandard word $\bf u$, as introduced in 2006 by de Luca and
De Luca, is given by a directive sequence of letters from an alphabet ${\cal
A}$ and by a directive sequence of involutory antimorphisms acting on ${\cal
A}^*$. Prefixes of $\bf u$ with increasing length are constructed using
pseudopalindromic closure operator.
  We show that generalized Thue--Morse words ${\bf t}_{b,m}$, with $b, m \in
\N$ and $b, m \geq 2$, are generalized pseudostandard words if and only if
${\bf t}_{b,m}$ is a periodic word or $b \leq m$. This extends the result of de
Luca and De Luca obtained for the classical Thue--Morse words.
