The reactivity of diatomic titanium with nitrous oxide has been studied in solid neon. Two molecules with the same Ti-2-N2O stoichiometry are identified from concentration, temperature, and irradiation effects. The more stable one is characterized by five fundamental vibrational transitions located below 1000 cm(-1), the high frequency one at 946 cm(-1) corresponding to a pure TiO stretching mode. Its structure, a rhombus OTiNTiN with the extra O atom fixed on one Ti, is confirmed by quantum chemical calculations, at the CCSD(T) level, which predict a C-s structure in the singlet state with a Ti-O bond length close to 1.66 angstrom, two nonequivalent Ti-N distances close to 1.94 and 1.75 angstrom, and a OTiTi angle of 119.2 degrees. The second Ti-2-N2O molecule, only observed after annealing, is easily converted into the first one upon irradiation above 12 000 cm(-1) and its kinetics of photoconversion allows vibrational transitions to be identified. The strongest one located at 2123.4 cm(-1) characterizes an N-N stretching mode. Corresponding ab initio calculations complete this picture with details on the electronic structure and allow us to identify a most adequate density functional to describe the spectroscopic properties of the studied species in a simpler broken-symmetry open-shell DFT context. The theoretical results predict the existence of a metastable product OTi2N2 and correctly account for the observed spectra of the various isotopic varieties.