Vibrational spectroscopic and average geometrical parameters of the strong H-bonded complexes [F(HF)₂]⁻ and [F(DF)₂]⁻ are determined for the first time from nine-dimensional (9D) perturbative and 6D variational calculations. The frequencies and intensities for all fundamental and some combination and overtone transitions obtained by the method of second-order vibrational perturbation theory (VPT2) are reported. A two-fold decrease in the H-F (D-F) stretching band frequency and a more than ten-fold increase in the intensity of this band upon complexation are predicted. The theoretical frequencies for both isolated isotopologues are in satisfactory agreement (to better than 70 cm⁻¹) with the scarce experimental data obtained in condensed phases. The main purpose of variational calculations is to analyze the intermode anharmonic coupling and the changes in the geometrical parameters upon vibrational excitation and H/D isotopic substitution. The equilibrium nuclear configuration and the 2D potential energy surface (PES) of [F(HF)₂]⁻ for H-F stretches are calculated in the MP2/6-311++G(3df,3pd), CCSD(T)/6-311++G(3df,3pd), CCSD(T)/aug-cc-pVTZ, and CCSD(T)/d-aug-cc-pVTZ approximations with the basis set superposition error taken into account. Anharmonic vibrational problems are solved by the variational method for 2D, 4D, and 6D systems of H-bond and H-F (D-F) stretches and in-plane bends. The VPT2 calculations and calculations of the PESs for 4D and 6D systems are performed in the MP2/6-311++G(3df,3pd) approximation. Comparison of variational anharmonic solutions for different vibrational subsystems demonstrates the influence of intermode anharmonic coupling on the mixing of wave functions and spectroscopic and geometrical characteristics. The inverse Ubbelohde effect is predicted and substantiated.