The production of nitrogen oxides (NOx) by lightning has been investigated with a three-dimensional cloud model. For the study of the NOx transport, the lightning NOx emissions are represented by a Lagrangian particle model instead of volume emissions. The advantages of this approach are (1) the transport of NOx inside the thunderstorm can be analyzed in great detail, (2) the NOx emissions can be represented as a line source instead of a volume emission, and (3) the comparison with high-resolution aircraft measurements can be conducted. This approach is applied to the 21 July 1998 supercell storm observed during the European Lightning Nitrogen Oxides project (EULINOX). Both, parameterized and observed cloud-to-ground and intracloud flash frequencies are used in the simulation and two different lightning NOx production rates are tested. The analysis shows that the parameterization using instantaneous cloud properties can approximately reproduce the lightning activity during the early mature phase of the intensifying storm but cannot be used for the complete life cycle. The comparison of the model results with aircraft NOx measurements indicate that the NOx production rate for intracloud lightning is equivalent or higher than that for cloud-to-ground flashes. Experimentally deduced values for the cloud-to-ground lightning NOx production of 4.9 kg(N), or equivalent 2.1 ¿ 1026 molecules NO, and a ratio between the intracloud and cloud-to-ground NOx production of 1.4 are confirmed by the model leading to an intracloud contribution to the total NOx production of up to 93%. For the applied production parameters 50% to 80% of the total lightning NOx is transported into the anvil, leading to a very pronounced C-shape profile. The estimated total NOx production by lightning during the lifetime of the storm is 22 t(N).