The spectroscopy of argon fluoride and krypton fluoride exciplexes in rare gas matrices is investigated using synchrotron radiation over the range of 50 to 600 nm. The diatomic Ar+F- and Kr+F- species are observed in excitation and emission spectra. Extensive vibrational progressions are observed in the excitation spectra and are used to determine the spectroscopic parameters of the ArF B state (T-e = 50233 cm(-1), omega(e) = 415.5 cm(-1), omega(e)x(e) = 3.1 cm(-1)) and D state (T-e = 51738 cm(-1), omega(e) = 476.7 cm(-1), omega(e)x(e) = 3.8 cm(-1)) and of the KrF B state (T-e = 39024 cm(-1), omega(e) = 342.4 cm(-1), omega(e)x(e) = 2.0 cm(-1)) and D state (T-e = 44479 cm(-1), omega(e) = 331.6 cm(-1), omega(e)x(e) = 1.4 cm(-1)). Lifetimes of 4 to 8 ns are measured for the diatomic emissions. A perturbed KrF species is observed which is identified in analogy to a similarly perturbed XeF species. Excitation spectra of the triatomic exciplexes Kr2+F- and Ar2+F- in neon are presented and described in terms of previous ab initio calculations. Emission and excitation of argon fluoride and krypton fluoride species in other matrices are presented. Large stimulated emission cross sections on the order of 10(-16) cm(2) are determined for the diatomic D-->X and B-->X emissions, which, together with nonradiative relaxation processes within the B and D states of ArF that efficiently populate the B(upsilon = 0) regardless of initial excitation, make ArF in neon a viable solid-state laser candidate.