In this paper we investigate the existence of the positive normalized solutions for the coupled Hartree–Fock type nonlocal elliptic system -Δu1-λ1u1=μ1∫RN|u1(y)|p1|x-y|N-αdy|u1|p1-2u1+βr1r1+r2∫RN|u2(y)|r2|x-y|N-αdy|u1|r1-2u1,-Δu2-λ2u2=μ2∫RN|u2(y)|p2|x-y|N-αdy|u2|p2-2u2+βr2r1+r2∫RN|u1(y)|r1|x-y|N-αdy|u2|r2-2u2,∫RN|u1|2dx=a12,∫RN|u2|2dx=a22,N≥3,a1,a2,μ1,μ2,β>0λ1λ2N=3p1=p2=α=2N+α+2N
0α∈(max{0,N-4},N)N+αN0λ1λ2N=3p1=p2=α=2N+α+2N0α∈(max{0,N-4},N)N+αN0λ1λ2N=3p1=p2=α=2N+α+2N0α∈(max{0,N-4},N)N+αN0λ1λ2N=3p1=p2=α=2N+α+2N0α∈(max{0,N-4},N)N+αN0λ1λ2N=3p1=p2=α=2N+α+2N0α∈(max{0,N-4},N)N+αN0λ1λ2N=3p1=p2=α=2N+α+2N0α∈(max{0,N-4},N)N+αN0λ1λ2N=3p1=p2=α=2N+α+2N0α∈(max{0,N-4},N)N+αN0λ1λ2N=3p1=p2=α=2N+α+2N0α∈(max{0,N-4},N)N+αN0λ1λ2N=3p1=p2=α=2N+α+2N0α∈(max{0,N-4},N)N+αN0λ1λ2N=3p1=p2=α=2N+α+2N0α∈(max{0,N-4},N)N+αN0λ1λ2N=3p1=p2=α=2N+α+2N0α∈(max{0,N-4},N)N+αN0λ1λ2N=3p1=p2=α=2N+α+2N0α∈(max{0,N-4},N)N+αN0λ1λ2N=3p1=p2=α=2N+α+2N0α∈(max{0,N-4},N)N+αN0λ1λ2N=3p1=p2=α=2N+α+2N0α∈(max{0,N-4},N)N+αN0λ1λ2N=3p1=p2=α=2N+α+2N0α∈(max{0,N-4},N)N+αN0λ1λ2N=3p1=p2=α=2N+α+2N0α∈(max{0,N-4},N)N+αN0λ1λ2N=3p1=p2=α=2N+α+2N0α∈(max{0,N-4},N)N+αN0λ1λ2N=3p1=p2=α=2N+α+2N0α∈(max{0,N-4},N)N+αN0λ1λ2N=3p1=p2=α=2N+α+2N0α∈(max{0,N-4},N)N+αN0λ1λ2N=3p1=p2=α=2N+α+2N0α∈(max{0,N-4},N)N+αN0λ1λ2N=3p1=p2=α=2N+α+2N0α∈(max{0,N-4},N)N+αN