Measurements of the ac susceptibility (ACS) as a function of frequency have been widely applied for the determination of structure parameters of magnetic nanoparticles (MNP). The analysis of spectra of real and imaginary parts measured on suspensions of MNP is generally based on the Debye model, extended by distributions of size parameters. Here, we compare different modifications of the Debye model with experimental data recorded on suspensions of single-core and multi-core iron-oxide nanoparticles. The applied models also depend on whether the nanoparticle's magnetic moments are thermally blocked and whether both Brownian and Néel relaxation have to be taken into account. The obtained core and hydrodynamic size parameters are compared with those from transmission electron microscopy and dynamic light scattering. Whereas structure parameters can be reliably determined for single-core nanoparticles, the interpretation of ACS spectra measured on multi-core nanoparticles is more complicated, especially regarding the contribution of particles relaxing via the Néel mechanism. Depending on the packing density and thus the interaction between cores in a particle, the effective core parameters derived from the spectrum must be interpreted with care.