  We consider different types of (local) products $f_1 f_2$ in Fourier Lebesgue
spaces. Furthermore, we prove the existence of such products for other
distributions satisfying appropriate wave-front properties. We also consider
semi-linear equations of the form $$ \qquad P(x,D)f = G(x,J_k f), $$ with
appropriate polynomials $P $ and $G$. If the solution locally belongs to
appropriate weighted Fourier Lebesgue space ${\mathscr F}L^q_{(\omega)} (\rr
d)$ and $P$ is non-characteristic at $(x_0,\xi_0),$ then we prove that
$(x_0,\xi_0)\not \in WF_{{\mathscr F}L^q_{(\widetilde {\omega})}} (f)$, where
$\widetilde{\omega}$ depends on $\omega$, $P$ and $G$.
