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Cooperative and noncooperative magnetization processes in magnetic nanostructures are investigated. Using model calculations it is shown that the Preisach model and related approaches, such as Henkel, ΔM, and ΔH plots, describe magnetism on a mean-field level and cannot account for intra- and inter-granular cooperative effects. For example, the ΔM plot of a nucleation-controlled two-domain particle gives the false impression of a positive intergranular interaction. A simple but nontrivial cooperative model, consisting of two interacting but nonequivalent particles, is used to show that cooperative effects are most pronounced for narrow switching-field distributions, i.e., for nearly rectangular loops. This is unfavorable from the point of magnetic recording, where one aims at combining narrow loops with a noncooperative local switching behavior. A general rule is that the neglect of cooperative effects leads to an overestimation of the coercivity.