AbstractIt is demonstrated that the fractional Hall plateaux, experimentally observed in some nearly ideal samples at very low temperatures, are manifestations of strongly correlated objects explicitly connected with Coleman's extreme case and Yang's concept of off‐diagonal long‐range order (ODLRO). This interpretation yields (n – 1)/(2n – 1), n = 2,3,… the most stable fractions. The appearance of large even fractions is considered together with a possible explanation of the recently observed fractional Hall states with even numerators in bilayer two‐dimensional electron systems. The present quantum correlations theory also suggests a theoretical analysis of the observed variations in wire‐wound reference resistors.