The magnetic phases of two concentrations of iron in Fe_xNi_1-xCl₂ (x=0.06 and 0.10) are reported from ⁵⁷Fe Mossbauer spectroscopy. Published data were used for x=0.06, and new data are presented for x=0.10. Substituting x=0.10 causes the ferrous moments to align along the crystallographic c-axis, whereas in pure NiCl₂ the moments are perpendicular to the c-axis. For x=0.06 parallel and perpendicular phases coexist, with the proportion of parallel moments decreasing smoothly from 74% at 4.2 K to zero at the Neel temperature (T_N). The introduction of iron reduces T_N from 52 K (x=0) to 46 K (x=0.10). A crystal field model was used to interpret temperature variations of the hyperfine parameters. The effective magnetic exchange constant for parallel moments is twice as large as that for perpendicular moments. In addition the Fermi contact constant B_c is -50 T for parallel moments, compared with 40 T for perpendicular moments. A 6 T magnetic field applied along the c-axis for x=0.10 at 5 K induces a canting of the moments from the principal electric field gradient axis by 20-35 degrees , and it is inferred that under these conditions the system is in a spin-flopped state in which the ferrous ions experience nearly identical environments.