The O-17 NMR chemical shift tensors for a dioxygen ligand bound to iron porphyrin model complexes, with or without inclusion of picket-fence-type substituents, have been calculated by density Functional IGLO approaches, based on structures optimized in Car-Parrinello molecular dynamics simulations. The calculations confirm the experimentally found, extremely large O-17 shifts, and the assignment of the higher-frequency signal to the terminal oxygen position. Metal-ligand pi-back-bonding and the presence of low-lying excited states influence the chemical shift tensors characteristically. The magnitude and orientation of the shift tensors also reflect the close analogy to the bonding in the ozone molecule. Possible explanations For the temperature dependence of the solid-state NMR spectra are discussed. The computed O-17 nuclear quadrupole coupling constants of ca. 11 MHz and ca. 17 MHz for bridging and terminal oxygen positions are close to the results for ozone, where theory and experiment agree well. This contradicts earlier assumptions of very small O-17 field gradients for picket-fence oxyheme models and raises some questions about the analysis of the solid-state O-17 NMR spectra. Possible reasons for the temperature dependence of the line widths in the solution spectra are suggested. We also discuss the implications of the O-17 NMR spectra for the nature of the ground state of oxyheme complexes.