Cerium-doped Cs$_2$LiYCl$_6$ (CLYC) and Cs$_2$LiLaBr$_x$Cl$_{6-x}$ (CLLBC) are scintillators in the elpasolite family that are attractive options for resource-constrained applications due to their ability to detect both gamma rays and neutrons within a single volume. Space-based detectors are one such application, however, the radiation environment in space can over time damage the crystal structure of the elpasolites, leading to degraded performance. We have exposed 4 samples each of CLYC and CLLBC to 800 MeV protons at the Los Alamos Neutron Science Center. The samples were irradiated with a total number of protons of 1.3$times$10$^{9}$, 1.3$times$10$^{10}$, 5.2$times$10$^{10}$, and 1.3$times$10$^{11}$, corresponding to estimated doses of 0.14, 1.46, 5.82, and 14.6 kRad, respectively on the CLYC samples and 0.14, 1.38, 5.52, and 13.8 kRad, respectively on the CLLBC samples. We report the impact these radiation doses have on the light output, activation, gamma-ray energy resolution, pulse shapes, and pulse-shape discrimination figure of merit for CLYC and CLLBC.