Mossbauer spectra of NH₄Co_0.994Fe_0.006Cl₃ have been recorded in the temperature range 1.3 to 250 K. The spectra are similar to those of isostructural CsCo_0.99Fe_0.01Cl₃ which is a quasi-one-dimensional Ising-like antiferromagnet. For NH₄Co_0.994Fe_0.006Cl₃ the transition to a partially disordered magnetic state occurs at T_N1=(27+or-2) K and to the fully magnetically ordered state at T_N1=(11+or-2) K. As for CsCo_0.99Fe_0.01Cl₃ the relaxation processes evident in the spectra were analysed using the stochastic model of Blume and Tjon with electronic relaxation occurring for Fe²⁺ in the three-dimensionally ordered chains below T_N1 and magnetic field reversal, attributed to solitons, in the one-dimensionally ordered chains in the partially disordered phase. Models developed for CsCo_0.99Fe_0.01Cl₃ were extended to include relaxation involving all the Fe²⁺ occupied electronic levels below T_N1 (i.e. the three lowest levels) and to allow both electronic and soliton relaxation to occur in the one-dimensionally ordered chains. The data for NH₄Co_0.994Fe_0.006Cl₃ and previous data for CsCo_0.99Fe_0.01Cl₃ were both analysed with these extended models. Relaxation rates were lower than those predicted theoretically for pure CsCoCl₃. This may be due to the presence of iron in the cobalt chains changing the soliton dynamics.