The AC magnetic properties of a sample of Fe3O4nanoparticles coated with oleic acid have been investigated with the help of AC susceptibility measurements. In particular, several DC magnetic fields have been superimposed on the AC field, and their effect on the magnetic response of the sample has been analysed. The results show the presence of a double peak structure in the imaginary component of the complex AC susceptibility measured as a function of the temperature. A preliminary evaluation of the Mydosh parameter for both peaks gives the information that each one of them is associated with a different state of interaction between nanoparticles. The two peaks evolve both in amplitude and position when the intensity of the DC field is changed. The field dependence of the peak position shows two different trends, and it is possible to study them in the framework of the currently existing theoretical models. In particular, a model of non-interacting magnetic nanoparticles has been used to describe the behaviour of the peak at lower temperatures, whereas the behaviour of the peak at higher temperatures has been analysed in the framework of a spin-glass-like model. The proposed analysis technique can be useful for the characterisation of magnetic nanoparticles used in several types of applications, such as biomedical and magnetic fluids.