We study some classes of infinite words that generalize standard episturmian words, defined by replacing the reversal operator with an arbitrary involutory antimorphism $\vartheta$ of $A^{*}$. An analysis of the relations occurring among such classes of words, and of the morphisms connecting them to standard episturmian words, is given. In particular, we analyse some structural properties of standard $\vartheta$-episturmian words and their characteristic morphisms.