We measured the densities of NH and NH2 radicals by cavity ring-clown spectroscopy in N-2-H-2 plasmas expanding from a remote thermal plasma source and in N-2 plasmas to which H-2 was added in the background. The NH radical was observed via transitions in the (0,0), (1,1), and (2,2) vibrational bands of the A(3)Pi <- X-3 Sigma(-) electronic transition and the NH2 radical via transitions in the (0,9,0) <- (0,0,0) band of the (A) over tilde (2) A(1)<- (X) over tilde B-2(1) electronic transition. The measurements revealed typical densities of 5 x 10(18) m(-3) for the NH radical in both plasmas and up to 7 x 10(18) m(-3) for the NH2 radical when N-2 and H-2 are both fed through the plasma source. In N-2 plasma with H-2 injected in the background, no NH2 was detected, indicating that the density is below our detection limit of 3 x 10(16) m(-3). The error in the measured densities is estimated to be around 20%. From the trends of the NHx radicals as a function of the relative H-2 flow to the total N-2 and H-2 flow at several positions in the expanding plasma beam, the key reactions for the formation of NH and NH2 have been determined. The NH radicals are mainly produced via the reaction of N atoms emitted by the plasma source with H-2 molecules with a minor contribution from the reaction of N+ with H-2. The NH2 radicals are formed by reactions of NH3 molecules, produced at the walls of the plasma reactor, and H atoms emitted by the plasma source. The NH radicals can also be produced by H abstraction of NH2 radicals. The flux densities of the NH, radicals with respect to the atomic radicals are appreciable in the first part of the expansion. Further downstream the NH, radicals are dissociated, and their densities become smaller than those of the atomic radicals. It is concluded that the NHx radicals play an important role as precursors for the N and H atoms, which are key to the surface production of N-2, H-2, and NH3 molecules.