An increase of the Nd~(3+) doping concentration and an enhancement of the laser induced fluorescence in the single crystal of YAlO_3: (Lu~(3+), Nd~(3+)) have been observed and are attributed to the size compensation effect. The low temperature (4.2K) fluorescence spectra indicate that the structure of the sharp lines arising from the radiative transitions of Nd~(3+) ions is not changed by the existence of Lu~(3+) ions, but the emission lines are inhomogeneously more broadened. Besides, it has been observed that the fluorescence due to the radiative transition from the Stark’s sublevel R_2 of the metastable level ~4F_(3/2) to the sublevels Y_1 of the manifold ~4I_(11/2) decreases with decreasing temperature and the fluorescence arising from the transitions R_1→Y_1 is relatively increased. The experimental fact is qualitatively interpreted. An increase of the Nd ~ (3 +) doping concentration and an enhancement of the laser induced fluorescence in the single crystal of YAlO_3: (Lu ~ (3+), Nd ~ (3+)) has been observed and are attributed to the size compensation effect. The low temperature (4.2K) fluorescence spectra indicate that the structure of the sharp lines arising from the radiative transitions of Nd ~ (3+) ions is not changed by the existence of Lu ~ (3+) ions, but the emission lines are inhomogeneously more broadened. Besides, it has been observed that the fluorescence due to the radiative transition from the Stark’s sublevel R_2 of the metastable level ~ 4F_ (3/2) to the sublevels Y_1 of the manifold ~ 4I_ (11 / 2) decreases with decreasing temperature and the fluorescence arising from the transitions R_1 → Y_1 is more increased. The experimental fact is qualitatively interpreted.