In order to examine the quantum size effects on the heavy-fermion behavior in CeAl2, we have performed measurements of the low-temperature specific heats for CeAl2 nanoparticles with average particle size 80 Angstrom for temperature down to 80mK. For 80 Angstrom - nanoparticles the magnitude of gamma of CeAl2 can be as high as 3600mJ/K-2 f.u. at T=80mK with TK approximate to 0.65K. Compared with the sharp anti-ferromagnetic order (T-N=3.8K) in bulk CeAl2 only a blurred peak at same temperatures is observed in CeAl2 nanoparticles. Due to the suppression of the long-range magnetic order by the limited geometric size and the less degeneracy of the density of states of conduction electrons D(epsilon(F)) the enhanced heavy-fermion behavior (in terms of gamma) and the disappearance of magnetic order in CeAl2 nanoparticles are attributed to the quantum size effects in nanoparticles. (C)1999 Acta Metallurgica Inc.