Abstract
We propose a new approach to the description of the anomalous temperature dependence of the quantum oscillations in strong magnetic field for the quasi–two-dimensional organic conductors (ET)2XHg(SCN)4,where X = K,Tl. Our model is based on the renormalisation of the g-factor due to the interaction of the conduction electrons with the weak magnetic moments in the sample and the presence of the strong correlation between the induced average magnetisation and an anomalous behaviour of the quantum oscillations of the resistivity and magnetisation.