  We define and study wave-front sets for weighted Fourier-Lebesgue spaces when
the weights are moderate with respect to the associated functions for general
sequences $\{ M_p\} $ which satisfy Komatsu's conditions $(M.1) - (M.3)'$. In
particular, when $\{ M_p\} $ is the Gevrey sequence ($M_p = p!^s$, $s>1$) we
recover some previously observed results. Furthermore, we consider wave-front
sets for modulation spaces in the same setting, and prove the invariance
property related to the Fourier-Lebesgue type wave-front sets.
