Isothermal magnetization curves, like hysteresis loops, initial curves, back field curves, acquisition curves and demagnetizing curves of isothermal remanent magnetization, are commonly used for rock magnetic purposes. In this study we investigate the relations among these curves and other useful magnetization curves (saturation initial curve and induced and remanent hysteretic magnetization curves) in order to compare coercivity and domain state parameters which can be derived from them. Most natural samples, especially sediments, are weakly magnetic and possess relatively stable Preisach functions. Their magnetization states can therefore be described by classical Preisach theory. This approach verifies well-known rules and establishes some formerly unreported relations between isothermal magnetization curves and parameters. It is possible to point out sets of mathematically independent isothermal magnetization curves and to state theoretical interrelations between dependent curves by simply inspecting Preisach diagrams. Furthermore, we define six elemental isothermal magnetization curves from a general partition scheme of the Preisach diagram. They can be easily obtained from common measurements and generate all above mentioned curves. The experimental applicability of our results is demonstrated for three (single-domain, pseudo-single-domain, multidomain) marine sediment samples. A physical rationale of the elemental curves reveals favorable properties for the investigation of interaction and domain state. As a spin-off from the general results, a new hysteresis-based procedure for the measurement of Hcr is presented. We also propose an apparently more robust hysteresis-derived domain state parameter and a generalized version of the well-known R parameter. All presented methods can be applied without actually measuring Preisach functions.¿ 1997 American Geophysical Union