Let's quickly gloss over the obvious dialectical relationship of these three terms (indeed, the dialectical relationship that is the key to altermodernity) despite H&N's protestations, and just get into how this sentence above is completely incoherent.
Now, hypermodernity here refers to theorists who feel that modernity is an unfinished project. And I can get to how they call it playfully German, considering the theorists they mostly identify with this position are Habermas and Beck.
Postmodernity they mean simply a rejection of modernity. Now, I don't understand how this is mostly a term of U.S. intellectuals. I can make some arguments for them, but they don't indicate anything useful in the text. Indeed, in a footnote they write: "The weak versions of postmodernism, from Jean-Francois Lyotard and Richard Rorty to Jean Baudrillard and Gianni Vattimo, offer this kind of aestheticized reaction to the crisis, at times veering into theology" (p. 403 n. 74). In that list we have two Frenchmen, one Italian, and one U.S. intellectual. Now, this might not be worth mentioning would it not be for the absurdity of referring to altermodernity as French.
For the several pages proceeding this schematic distinction between the three reactions of failed modernity, they had been discussing concrete political assemblages they would associate with altermodernity, and host of theorists to explain altermodernity. Almost to a person we are talking about Latin American and Caribbean theorists and struggles. How does this suddenly become a French thing? The only French theorist they have specifically named with altermodernity up to that point is Foucault. On the pages before and afterward they warn against the dangers of Eurocentrism, and then we have this completely bizarre and unwarranted moment of Eurocentrism.