  In this paper, we present the complex interpolation of Besov and
Triebel-Lizorkin spaces with generalized smoothness. In some particular cases
these function spaces are just weighted Besov and Triebel-Lizorkin spaces. An
application, we obtain the complex interpolation between the weighted
Triebel-Lizorkin spaces $\dot{F}_{p_{0},q_{0}}^{s_{0}}(\omega_{0})$ and
$\dot{F}_{\infty ,q_{1}}^{s_{1}}(\omega_{1})\ $with suitable assumptions on the
parameters $\ s_{0},s_{1},p_{0},$ $q_{0}$ and$\ q_{1}$, and the pair of weights
$(\omega_{0},\omega_{1})$.
