In this paper we report on electron paramagnetic resonance (EPR) of paramagnetic centers in the carbonaceous matter of primitive siliceous rocks, known to contain the most ancient traces of life. The EPR lines observed are attributed to π-radicals stabilized by the aromatic structure of this matter. It is found that the line widths and the line shapes vary continuously during geological periods and show a progressive pattern evolution from Gaussian–Lorentzian (recent) to purely Lorentzian (ca. 2000 million years [Myr]), and to supra-Lorentzian (ca. 3500 Myr). Artificial ageing experiments allowed us to define four stages of maturation of the organic matter according to the evolution of g-factors, EPR intensity, peak-to-peak line width and line shape. We suggest that the peculiar supra-Lorentzian line shape observed for organic matter older than 2000 Myr should be related to a low-dimensional (two- or one-dimensional) spatial distribution of electron spins. From these results, we derive a relationship between the line shape and the age of the organic matter, valid for ages ranging from about 600 Myr to about 3500 Myr.