GaAs/GaAlAs quantum wires grown by modulated flow rate metalorganic chemical vapour deposition were investigated by spatially resolved photoluminescence spectroscopy using a scanning near-field optical microscope. It was found that the wires decompose into a series of regions that emit luminescence of varying intensity. The spectra of these regions feature several narrow emission lines, which means that there is a series of more or less localised exciton states inside each region. It is expected that these exciton states are very close to each other and are correlated, which leads to level repulsion. The mean autocorrelation function taken from a series of near-field spectra clearly reveals this level repulsion, which amounts to roughly 2 meV.