  We prove an asymptotic formula for the second moment of a product of two
Dirichlet L-functions on the critical line, which has a power saving in the
error term and which is uniform with respect to the involved Dirichlet
characters. As special cases we give uniform asymptotic formulae for the fourth
moment of individual Dirichlet L-functions and for the second moment of
Dedekind zeta functions of quadratic number fields on the critical line.
