Hemoglobin (Hb) is the prototypical example of a cooperative protein. Cooperativity of Hb is largely accounted for by the oxygen-linked allosteric interconversion between the T and R states/structures. Allostery is such a powerful explanation of Hb cooperativity that the possibility of cooperative events occurring within each allosteric conformation, in the absence of any quaternary structural change has usually been overlooked, and actually experiments specifically aimed at detecting non-allosteric cooperativity have usually failed to do so. However there are strong, but often neglected, theoretical reasons pointing to the presence of non-allosteric cooperativity under common experimental conditions, that have recently raised new interest and have been thoroughly re-investigated. Non-allosteric cooperativity within T state Hb has often been invoked to describe puzzling experimental data, either as an intrinsic property of the macromolecule or as a consequence of the binding of non-heme ligands. Few convincing pieces of evidence exist for the former hypothesis, whereas very strong proofs are available for effector-induced non-allosteric cooperativity in hemoglobin. Moreover, non-allosteric cooperativity in (T)Hb may explain some hitherto puzzling findings, e.g. the bi-exponential O-2 release from (T)Hb observed by Q.H. Gibson in oxygen pulse experiments, the invariance of L-4 found by K. Imai, the cooperative ligand binding by crystals of T state Hb Rotschild, and, possibly, the cooperativity observed in at least some mixed metal hybrid Hbs.