Abstract We analyze the possible existence of a superconducting state in a background with long-range antiferromagnetism. We consider a generalized Hubbard model with nearest-neighbor correlated hopping in a square lattice. Near half filling, the model exhibits a d-wave-Bardeen–Cooper–Schrieffer (BCS) solution in the paramagnetic state. The superconducting solution would be enhanced by the antiferromagnetic background if the contribution of triplet pairs with d-wave symmetry and total momentum ( π, π) could be neglected. However, we find that due to their contribution, the coexistence of superconductivity and long-range antiferromagnetism is ruled out for large values of the Coulomb repulsion U. Spin-density wave fluctuations (SDWF) do not change this result.