In my experience, these will quickly form green spot and and green thread/hair algae if you expose them to high light. In a high light tank, you can shade or partially shade them with other taller plants or with some floating plants and that should prevent the problem as long as your other parameters(consistent and proper c02 levels and adequate ferts) are in order.
I have a high light tank with anubias, and they did get GSA pretty bad. I have upped my phospates, and now it is in check. They aren't shaded too well either.