In this work we investigate the single- and the double-spin asymmetries at the collisions of polarized protons pp → (γ
0, Z′) + X within the scope of QCD, the electroweak interaction and superstring E
6 theory. The helicity amplitude method is used. Analytical expressions for the single- and the double-spin asymmetries are obtained and their dependence on the transverse momentum of the lepton pair is investigated at the three different values of invariant masses of the lepton pair. The pure contribution coming from the superstring Z′ boson on the single- and double- spin asymmetries has been extracted. The results obtained allow investigation of the spin structure of the proton.