Quantum chemical calculations suggest that a series of molecules with the general formula cyclo-M-n(mu-H)(n) (M = Ag, Au; n = 3-6) are stable. All cyclo-MnHn species, except cyclo-Au3H3, have the same symmetry with the respective aromatic hydrocarbons but differ in that the hydrogen atoms are in bridging positions between the metal atoms and not in terminal positions. The aromaticity of the hydrosilver(I) and hydrogold(I) analogues of aromatic hydrocarbons was verified by a number of established criteria of aromaticity, such as structural, energetic, magnetic, and chemical criteria. In particular, the nucleus-independent chemical shift, the relative hardness, Deltaeta, the electrophilicity index, omega, and the chemical reactivity toward electrophiles are indicative for the aromaticity of the hydrosilvers(l) and hydrogolds(l). A comprehensive study of the structural, energetic, spectroscopic (IR, NMR, electronic, and photoelectron spectra), and bonding properties of the novel classes of inorganic compounds containing bonds that are characterized by a common ring-shaped electron density, more commonly seen in organic molecules, is presented.