Precise oxygen equilibrium curves for carp hemoglobin were determined at 15 °C in bis-Tris buffer, and in phosphate buffer in the presence and absence of P6-inositol, and at various temperatures in phosphate buffer. Parameters of the Koshland, Némethy and Filmer (1966) (KNF) simple, sequential models (square and tetrahedral) were estimated by non-linear least-square fit of the experimental data to Hill plots. Non-, negative and positive co-operativity can be fitted by the KNF models. Considering equilibrium arguments, K2 AB KBB, the KNF parameter governing the co-operativity of the system, predicts a symmetry conserved mode of action in regions of high, positive co-operativity, and a symmetry non-conserved mode of action in regions of low, non- or negative co-operativity. The simple, sequential, square KNF model fits better the Hill plots than does the simple, sequential, tetrahedral KNF model. From the effect of temperature on carp hemoglobin in phosphate buffer, the heats and entropies of the subunit interaction parameter, K2 AB KBB, and of the oxygenation parameters, KBBKxBKtAB and K 3 2 BBKxBKtAB, for the square and tetrahedral models, respectively, were calculated and show the square model to account well for previously published data on the carp hemoglobin molecule. This study indicates that the KNF model, in its simplest form, is capable of explaining many of the functional properties of cooperative systems, as opposed to the Monod, Wyman and Changeux (1965) model which seems only to be a special case of the KNF model in regions of high, positive co-operativity.