The nature of intrinsic luminescence of Y3Ga5O12 (YGG) and (LaLu)3Lu2Ga3O12 (LLGG) single crystals grown from a melt was determined. In the case of a YGG single crystal containing YGa antisite defects with a concentration of 0.25–0.275 at. % the intrinsic luminescence was considered as a superposition of luminescence of self-trapped excitons (STE), luminescence of excitons localized near antisite defects (LE(AD) centers) and luminescence caused by a recombination of an electron with a hole captured at YGa antisite defects. Due to a large (2–3 % ) concentration of LuLa antisite defects in LLGG single crystals the intrinsic luminescence was a superposition mainly of the LE(AD) center emission and the recombination luminescence of LuLa antisite defects. The energy structure of the mentioned centers in YGG and LGGG hosts was determined from the excitation spectra of their luminescence under excitation by synchrotron radiation in the range of the fundamental absorption edge of these garnets.