I don't know what sex they are but my smaller one bobs its head when it sees the other one?
What your anole is displaying is most likely a territorial display. he is showing who is the alpha but, there is a good chance it just might be a mating display. I would bring them into a local pet store and have them looked at for gender and ask for more information on whats going on.
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. According to Breeding Anoles, head-bobbing and showing the dewlap are mating displays.
Then he's probably a male. And males will "bob" at the site of any other anole, just in case.
I'd bet on territorial display and/or "I'm big enough to hurt you; don't try to eat me". (Most reptiles divide things into it-eats-me, I-eat-it, and rock. Humans are warm rocks.)
. Not very picky, eh?