In this work, we clarify the nature of a previously not precisely identified Fermi dyad in the frequency range around 1600 cm(-1) in oligo( para-phenylenes). To this end, we deploy a novel method to calculate third order anharmonic coupling effects in molecules. This Fermi dyad is shown to yield important information on the structural properties of the investigated materials. The nature of all vibrations contributing to this quantum mechanical resonance phenomenon is explained on the basis of a detailed normal coordinate analysis. The anharmonic coupling is then closely investigated by applying our theoretical model. In particular, we discuss the intensity redistribution among the two components of the Fermi doublet as well as their energetic separation. Subsequently, we establish a relation between these features and the structural conformation of the molecules. We show, how oligomer length and planarity of these systems can be determined from experimental Raman spectra by extracting the positions and relative intensities of the two components of the Fermi doublet. Furthermore, this Fermi resonance is shown to be sensitive to chemical modification on the molecules such as deuteration or substitution. Finally, we extend our model to electronically excited states in this class of molecules, as well as to charged species.