  We study the 2k-th power moment of Dirichlet L-functions L(s,\chi) at the
centre of the critical strip (s=1/2), where the average is over all primitive
characters \chi (mod q). We extend to this case the hybrid Euler-Hadamard
product results of Gonek, Hughes & Keating for the Riemann zeta function. This
allows us to recover conjectures for the moments based on random matrix models,
incorporating the arithmetical terms in a natural way.
