The quality of the Hartree-Fock and the density functional methods for the description of hydrogen bonds is judged by comparing quantitatively the outcome of calculations on the hydrogen bonds in ammonium (bi)fluorides with the results of accurate electron density studies by X-ray diffraction. X-ray data and analysis for NH4F were taken from the literature; those for NH4HF2 were collected in a single-crystal diffraction experiment. A total of 8522 reflections was measured, yielding the structure factors of 2333 independent reflections. R-int (F-2) = 0.03. A multipole refinement converged to R-w (F2) = 0.034. Quantum chemical calculations were carried out with the CRYSTAL, package, using the Hartree-Fock and the density functional methods and a 6-311G** basis set. Both the local density and the generalized gradient(GGA) version of the latter were applied. To make a comparison with experiment valid, the theoretical densities were converted to structure factors that then were subjected to the same multipole refinement as the experimental ones. The differences between the theoretical and the experimental results are shown-by comparing in direct space the electron density in the bonding regions in the crystals and the topological characteristics at the bond critical points, in reciprocal space the structure factors as functions of the scattering angle; The GGA results showed the best agreement with experiment, with excellent agreement both in the very short and the longer hydrogen bends. The curvatures of the electron density distributions along the hydrogen bonds and perpendicular to it reveal the character of these bonds.