Ba_1-xGd_xF_2+x, Sr_1-xGd _xF_2+x, and Sr_1-xLa_xF_2+x systems with fluorite-type structure (0 < x < 0.25), and La _1-xBa_xF_3-x system with tysonite-type structure (x = 0 and x = 0.0185) were simulated by the constant-temperature molecular dynamics (MD) method in the temperature range T = 500-2100 K that includes the superionic transition and melting points. A simple Born-Mayer-Huggins model potential was used. The internal energy, anion diffusion coefficients, spatial distribution and characteristics of movement of fluoride ions were calculated. For Ba_1-xGd_xF_2+x, a satisfactory agreement between simulation results and experimental data was obtained, while for the Sr-containing systems, the model potential should be improved substantially. For La_1-xBa_xF_3-x, it was found that to reproduce properties of the superionic phase satisfactorily, defects are to be included explicitly in the model, and when that is done, already a simple model gives a good agreement with experiment; thus, it is confirmed that properties of tysonite-type phases are sensitive to nature and concentration of defects.