We present LEED, AES and thermal desorption studies on the behaviour of atomic nitrogen layers, deposited on Rh(110)1 x 1 and Rh(110)1 x 2 surfaces by NO + H-2 reaction at 450 K. The desorption measurements are performed in two modes, with a linear temperature ramp (TPD) and at constant temperature. The N2 TPD spectra are used for evaluation of the desorption parameters. The LEED patterns change sequentially from a streaky 3 x 1 to 2 x 1 with growth of the nitrogen layer on Rh(110)1 x 1. The sharpness of the extra spots increases after heating to 480 K or when the layers are produced in a partial desorption mode. This indicates that the formation of well ordered structures is an activated process. The better ordering leads to higher thermal stability of the layers, as reflected by the increase of the desorption energies from 90 to 130 kJ/mol. The N2 TPD spectra are very sharp and are best fitted to a zero order rate process. The changes in the desorption kinetics at a constant temperature are attributed to competing desorption from 2 x 1, 3 x 1 and disordered phases, coexisting on the surface within certain coverage range. Nitrogen layers deposited on Rh(110)1 x 2 at T less-than-or-equal-to 400 K form a (2 x 2)pg structure. At T > 440 K the 1 x 2 reconstruction is lifted and the (2 x 2)pg structure converts sequentially into the same 2 x 1, 3 x 1 and 1 x 1 structures, observed for nitrogen adsorbed on Rh(110)1 x 1. We suggest that the 2 x 1, 3 x 1 and (2 x 2)pg structures involve N-induced restructuring of the substrate surface with some nitrogen penetrating underlayer.