The high-pressure and high-temperature behaviors of LiF and NaF have been studied up to 37 GPa and 1000K. No phase transformations have been observed for LiF up to the maximum pressure reached. The B I to 132 transition of NaF at room temperature was observed at similar to 28 GPa, this transition pressure decreases with temperature. Unit-cell volumes of LiF and NaF B I phase measured at various pressures and temperatures were fitted using a P-V-T Birch-Murnaghan equation of state. For LiF, the determined parameters are: alpha(0) = 1.05(3) x 10(-4) K-1, dK/dT = -0.025 (2) GPa/K, V-0 = 65.7 (1) angstrom(3), K-0 = 73 (2) GPa, and K' = 3.9 (2). For NaF, alpha(0) = 1.34 (4) x 10(-4) K-1, dK/dT = -0.020 (1) GPa/K, V-0 = 100.2 (2) angstrom(3), K-0 = 46(1) GPa, and K' = 4.5 (1).