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The authors present measurements of photoluminescence spectra and imaging of the sharp emission lines which result from the radiative recombination of excitons trapped in compositional fluctuations in dilute nitride epitaxial layers and quantum wells, using low-temperature near-field scanning optical microscopy (NSOM). Both weak and strong localisation (i.e. quantum-dot-like emission) are observed for samples of GaAsN and InGaAsN, with little difference depending on the presence or absence of In. Localisation energies are in the range 10-60 meV. Zeeman splitting and diamagnetic shifts are observed in the near-field magneto-photoluminescence, and from these effects the size (r=3-17 nm), composition fluctuations (Δy ∼0.5%) and density (100-1000 μm-3) of the compositional clusters are determined. Using two-dimensional NSOM images, the authors observe a strong lateral inhomogeneity for the GaAsN epilayers resulting from nitrogen clustering. A one-dimensional compositional modulation along the  direction is also observed for a GaAsSbN quantum well on the length scale of 100 nm. Transmission electron micrographs confirm the existence of these spatial nonuniformities. Time-resolved spectroscopy has also been carried out on one of the samples reported here (In0.08GaAsN0.03). Pump-and-probe photoluminescence experiments provide the following time constants: the exciton relaxation time to the ground states of the localisation regions is found to be ∼40-70 ps as the emission varies from high to low energy, and the time for depopulation of these localised states is 2-4 ns.