  In this paper we study the existence of a unique solution to a general class
of Young delay differential equations driven by a H\"older continuous function
with parameter greater that 1/2 via the Young integration setting. Then some
estimates of the solution are obtained, which allow to show that the solution
of a delay differential equation driven by a fractional Brownian motion (fBm)
with Hurst parameter H>1/2 has a smooth density. To this purpose, we use
Malliavin calculus based on the Frechet differentiability in the directions of
the reproducing kernel Hilbert space associated with fBm.
