Previous Mössbauer studies of the FeₓNi₁₋ₓCl₂ system led to conflicting hypothesises about the exact magnetic behaviour of the Fe₲⁺ ions in the mixed magnetic phase. This phase occurs between the Fe₲⁺ concentration values of x=0.03 and 0.12, and at temperatures less than 45 K. Tamaki and Ito (1991,1993) used a model which had co-existing magnetic order, with some Fe₲⁺ and Ni₲⁺ spins aligned near the crystalline c axis, while the others aligned near the perpendicular xy plane (model1). The relative population of the two sites is dependent on the concentration x and the temperature. Pollard et al (1982,1991) used a similar model, but with the spins aligned parallel to the x axis or in the xy plane (model 2). Again, the populations of the two sites depended on x and temperature. New Mössbauer studies were done, and the results are displayed and discussed in this thesis. The new studies concerned mixtures within the mixed phase (x=0.031 and 0.052) and the pure anti-ferromagnetic phase (x=0.15). Models 1 and 2 both generated similar simulated spectra, which gave similar fits to the experimental spectra. Model 1 generated spectra which fit only marginally better than model 2 spectra. Therefore it was not possible to conclude which model gave a better description of the FeₓNi₁₋ₓCl₂ system, using the new Mössbauer studies. Monte Carlo studies were also done, to provide a possible explanation for the complex magnetic behaviour which occurs in the mixed phase of FeₓNi₁₋ₓCl₂. The results showed that a random distribution of metal ions does not create co-existing spin order. However, clusters of Fe₲⁺ ions embedded in regions of FeₓNi₁₋ₓCl₂ with low values of x did create co-existing magnetic order. The spins aligned near the crystalline c axis or the xy plane, in agreement with model 1. Hence it was concluded that an un-even distribution of metal ions in FeₓNi₁₋ₓCl₂ exists, and directs the complex mixed phase behaviour which has been observed experimentally by workers using Mössbauer spectroscopy and Neutron diffraction techniques. The Monte Carlo programs mentioned in this thesis were written by the Author.