The optical properties of Tb(3+) ions in oxyorthosilicates of lutetium and yttrium (LYSO) are reported. The introduction of a small number of terbium ions (nominal content 10 ppm) generates, in the otherwise transparent absorption spectrum of the matrix, an ultraviolet absorption band peaked at about 240 nm. By exciting within the reported UV band, line shaped emissions in the 350-600 nm range are detected. These transitions are related to the (5)D(3) and (5)D(4) levels of the Tb(3+) ions and are characterized by decay times in the millisecond time domain. Analysis of the decay time measurements allows us to individuate a cross relaxation mechanism among terbium ions even at the low dopant concentration investigated. We propose a three-level kinetic model which is able to successfully reproduce the experimental data, allowing us to discriminate among the radiative and non-radiative contributions to the observed emissions.