Let ω1, ω2 be slowly increasing functions and let ω3 be weight function on ℝn. In section 2 we define a bilinear multiplier from L(p1, q1, ω1dμ) (ℝn) × L(p2, q2, ω2dμ) (ℝn) to L(p3, q3, ω3dμ) (ℝn) by a bounded operator Bm, where 1≤ p1, p2, p3, q1, q2, q3 < ∞ and m (ξ,η) is a bounded, measurable function on ℝn × ℝn. We denote the space of bilinear multipliers of this type by BM (L(p1, q1, ω1dμ) × L(p2, q2, ω2dμ), L(p3, q3, ω3dμ)), and study of the basic properties of this space. We give methods of construction examples of bilinear multipliers. Similarly in section 3, by using variable exponent Lorentz space, we define the bilinear multipliers from L( p1 (x), q1 (x)) × L( p2 (x), q2 (x)) to L( p3 (x), q3 (x)) and discuss basic properties of the space of bilinear multipliers BM (L( p1 (x), q1 (x)) × L( p2 (x), q2 (x)), L( p3 (x), q3 (x))).