Abstract: Starting from an initial sequence of Hermite elements, a Hermite subdivision scheme recursively generates finer sequences of Hermite elements which are associated with the dyadic points. With the help of the interpolating splines that can be associated with the Hermite elements, we analyze the smoothness of the limit curves generated by Hermite subdivision schemes of arbitrary order, including non-interpolatory ones. After presenting these theoretical results, we describe two new families of Hermite subdivision schemes.