Zero-field aggregation of magnetic nanoparticles in a ferrofluid can either be irreversible or result from a dynamic equilibrium; the two cases can be distinguished by measurements of the complex magnetic susceptibility and by cryogenic transmission electron microscopy (cryo-TEM). We demonstrate this by comparing two colloidal systems that show dipolar structure formation in zero field. A dispersion of magnetic iron nanoparticles is gradually oxidized to decrease the magnetic moments, and despite the vanishing dipolar attractions, thermal motion does not break up the dipolar structures into single particles. Instead, the dipolar structures become chemically fixed during the oxidation process, an example of irreversible aggregation. In contrast, the zero-field dipolar structures in a chemically stable magnetite dispersion are found to disintegrate upon dilution, indicating that the structures are reversible and result from a dynamic equilibrium. r