Abstract: A group G is said to have the Magnus property if the following holds: whenever two elements x, y have the same normal closure, then x is conjugate to y or to y −1. We prove: let p be an odd prime, and let G, H be residually finite-p groups with the Magnus property. Then the direct product $${G \times H}$$ has the Magnus property. By considering suitable crystallographic groups, we give an explicit example of finitely generated, torsion-free, residually finite groups G, H with the Magnus property such that the direct product $${G \times H}$$ does not have the Magnus property.