We study the hadronic eta' -> pi pi decays within the framework of U(3)_L X U(3)_R Chiral Perturbation Theory including resonance states and the complete one-loop corrections. 
The amplitude is projected in partial waves and unitarized by means of the N/D method resumming both the important pi pi and the subleading pi eta final-state interactions.
The unknown scalar resonance input parameters, coupling strengths and masses, are determined from fits to the Dalitz plot experimental data recently released by the A2 collaboration.
As a byproduct of our analysis, the associated Dalitz slope parameters are found to be a=-0.073(7)(5), b=-0.052(1)(2), d=-0.052(8)(5), which lie in the ballpark of the current experimental and theoretical determinations.
We hope our results to be of relevance for present experimental analyses of these decays.