  Let $q$ be a positive integer ($\geq 2$), $\chi$ be a Dirichlet character
modulo $q$, $L(s, \chi)$ be the attached Dirichlet $L$-function, and let
$L^\prime(s, \chi)$ denote its derivative with respect to the complex variable
$s$. Let $t_0$ be any fixed real number. The main purpose of this paper is to
give an asymptotic formula for the $2k$-th power mean value of
$\left|(L^\prime/L)(1+it_0, \chi)\right|$ when $\chi$ runs over all Dirichlet
characters modulo $q$ (except the principal character when $t_0=0$).
