When a Ne: HF mixture is subjected to Penning ionization and/or photoionization by neon atoms in their first excited states, between 16.6 and 16.85 eV, and the products are rapidly frozen at approximately 5 K, the infrared spectrum of the resulting deposit includes absorptions assigned to NeHF+ and HFFH+. Evidence is presented suggesting that neon-matrix shifts may be anomalously large for protonated molecules which are derived from species with proton affinities near or below 550 kJ/mol. The results of earlier ab initio studies, as well as those of the present experimental and ab initio studies, indicate that the NeHF+ complex is quite strongly bound. The nu(3) absorptions of NeHF+ and NeDF+ and the nu(1) + nu(3) absorption of NeHF+ are tentatively identified. An absorption at 3064.7 cm(-1) has isotopic substitution behavior appropriate for its assignment to HFFH+. Density functional calculations were performed in order to estimate the positions of the harmonic vibrational fundamentals of HFFH+-d(n), and a more elaborate two-dimensional calculation on the HF-stretching potential surface was conducted in an attempt to take into account the large anharmonic contribution. Processes which occur on ultraviolet irradiation of the deposit are considered.