A laser-induced fluorescence technique, in combination with optical emission spectroscopy, was applied to investigate the spatial distribution of the number densities of neutral species in an asymmetric low-pressure 27.12 MHz discharge in pure nitrogen. The primary targets of this investigation were the three nitrogen triplet states C 3 u , B 3 g and the metastable A 3 + u each in their lowest vibrational levels v = 0, 1, 2 and additionally v = 8 of A 3 + u which can be populated very efficiently in the plasma sheath. The absolute number densities of all these states were determined in a Rayleigh scattering experiment, the results of which have been published elsewhere (Krames B, Glenewinkel-Meyer T and Meichsner J 2001 J. Appl. Phys. 89 3115). The spatial profiles as a function of the discharge parameters were studied by varying the gas pressure between 10 and 100 Pa and the effective rf voltage up to 260 V. These profiles of the different molecular states vary markedly in the plasma bulk as well as in the sheath near the powered electrode. A model, which includes the production, diffusion and quenching rates of contributing species and also fluorescence cascade processes, explains these varieties. A comparison with the experimental data at 50 Pa confirms the results of the model calculations.