Abstract: It is a well-known fact that if G and H are groups of homeomorphisms of the interval or of the circle, then the free product G*H is also a group of homeomorphisms of the interval or of the circle, respectively. I will discuss higher regularity of group actions, showing that if G and H are groups of C^{\infty} diffeomorphisms of the interval or of the circle, then G*H may fail to act by even C^2 diffeomorphisms on any compact one-manifold. As a corollary, we can classify the right-angled Artin groups which admit faithful C^2 actions on the circle, and recover a joint result with H. Baik and S. Kim. This is joint work with S. Kim.