In this paper we study some classes of infinite words generalizing episturmian words, and analyse the relations occurring among such classes. In each case, the reversal operator $R$ is replaced by an arbitrary involutory antimorphism $\vartheta$ of the free monoid $A^{*}$. In particular, we define the class of $\vartheta$-words with seed, whose “standard” elements ($\vartheta$-standard words with seed) are constructed by an iterative $\vartheta$-palindrome closure process, starting from a finite word $u_0$ called the seed. When the seed is empty, one obtains $\vartheta$-words; episturmian words are exactly the $R$-words. One of the main theorems of the paper characterizes $\vartheta$-words with seed as infinite words closed under $\vartheta$ and having at most one left special factor of each length $n\geq N$ (where $N$ is some nonnegative integer depending on the word). When $N=0$ we call such words $\vartheta$-episturmian. Further results on the structure of $\vartheta$-episturmian words are proved. In particular, some relationships between $\vartheta$-words (with or without seed) and $\vartheta$-episturmian words are shown.