Let ω,ω ₀ be appropriate weight functions and q∈[1,∞]. We introduce the wave-front set, WFFLq(ω)(f) of f∈S′ with respect to weighted Fourier Lebesgue space FLq(ω). We prove that usual mapping properties for pseudo-differential operators Op (a) with symbols a in S(ω0)ρ,0

hold for such wave-front sets. Especially we prove that

WFFLq(ω/ω0)(Op(a)f)⊆⊆WFFLq(ω)(f)WFFLq(ω/ω0)(Op(a)f)∪Char(a). (*)

Here Char (a) is the set of characteristic points of a.