Quantum confinement effects and nonlinear luminescence of excitons in CuI microcrystallites on the substrates of poly-methyl methacrylate have been studied. Exciton transitions due to the hexagonal structure appear in the disk-shaped microcrystallites. The confinements of the relative motion of excitons in the hexagonal structure induce remarkable blue-shifts of the transition energy. From the size dependence of their confinement energies, reduced mass ratios of the hexagonal excitons were obtained. Under high-density excitation, a new luminescence band grows super-linearly at the energy position lower by similar to 30 meV than the exciton resonance. The origin of the luminescence was assigned to an annihilation of bi-excitons in the hexagonal structure. (C) 2000 Elsevier Science B.V. All rights reserved.