This paper is concerned with the following parabolic-parabolic-elliptic chemotaxis system with singular sensitivity and Lotka-Volterra competitive kinetics, (0.1) { u t = Δ u − χ 1 ∇ ⋅ (u w ∇ w) + u (a 1 − b 1 u − c 1 v) , x ∈ Ω v t = Δ v − χ 2 ∇ ⋅ (v w ∇ w) + v (a 2 − b 2 v − c 2 u) , x ∈ Ω 0 = Δ w − μ w + ν u + λ v , x ∈ Ω ∂ u ∂ n = ∂ v ∂ n = ∂ w ∂ n = 0 , x ∈ ∂ Ω , where Ω ⊂ R N is a bounded smooth domain, and χ i , a i , b i , c i (i = 1 , 2) and μ , ν , λ are positive constants. This is the first work on two-species chemotaxis-competition system with singular sensitivity and Lotka-Volterra competitive kinetics. Among others, we prove that for any given nonnegative initial data u 0 , v 0 ∈ C 0 (Ω ¯) with u 0 + v 0 ≢ 0 , (0.1) has a unique globally defined classical solution (u (t , x ; u 0 , v 0) , v (t , x ; u 0 , v 0) , w (t , x ; u 0 , v 0)) with u (0 , x ; u 0 , v 0) = u 0 (x) and v (0 , x ; u 0 , v 0) = v 0 (x) in any space dimensional setting with any positive constants χ i , a i , b i , c i (i = 1 , 2) and μ , ν , λ. Moreover, we prove that there is χ ⁎ (μ , χ 1 , χ 2) > 0 satisfying χ ⁎ (μ , χ 1 , χ 2) = { μ χ 2 4 if 0 < χ < 2 μ (χ − 1) if χ ≥ 2 , when χ 1 = χ 2 : = χ and χ ⁎ (μ , χ 1 , χ 2) ≤ min { μ χ 2 + μ (χ 1 − χ 2) 2 4 , μ χ 1 + μ (χ 2 − χ 1) 2 4 } , when χ 1 ≠ χ 2 such that the condition min { a 1 , a 2 } > χ ⁎ (μ , χ 1 , χ 2) implies lim sup t → ∞ ‖ u (t , ⋅ ; u 0 , v 0) + v (t , ⋅ ; u 0 , v 0) ‖ ∞ ≤ M ⁎ and lim inf t → ∞ inf x ∈ Ω (u (t , x , u 0 , v 0) + v (t , x ; u 0 , v 0)) ≥ m ⁎ for some positive constants M ⁎ , m ⁎ independent of u 0 , v 0 , the latter is referred to as combined pointwise persistence. [ABSTRACT FROM AUTHOR]