We extend the turbo demodulation procedure proposed by Li and Ritcey (see IEEE Journal on Selected Areas in Communications, vol.17, no.4, p.715-24, 1999) and by Magniez, Muquet, Duhamel, Buzenac and de Courville (see Proc. Int. Symp. on Turbo Codes and Related Topics, Brest, France, p.169-72, 2000) to OFDM systems with cyclic prefix (CP-OFDM) or zero-padding (ZP-OFDM). The extensions account for the noise color introduced by linear equalization. Resorting to realistic simulations, we also show that the turbo demodulation procedure used with set partitioned labeling can significantly outperform non-iterative decoding with Gray labeling. We also show that the proposed turbo demodulation scheme increases the performance gap between ZP and CP-OFDM relative to non-iterative decoding because it amplifies the performance gain brought by the guaranteed symbol recovery of ZP-OFDM.