Low-field susceptibility measurements show that Ce1−xGdxAl3 exhibits spin-glass-like behavior over nearly the entire concentration range. The temperatures of the spin-glass-like transition Tm(x) are surprisingly high [Tm(0.635)=125 K] considering that none of the rare-earth trialuminides order above 25 K. The Ce is necessary for the anomalous behavior since it is absent in (La, Gd)Al3. For x≤0.23, T≤5 K there is an interplay between the heavy-fermion and spin-glass-like behavior. The values of Tm would probably not be so large if the system were not a heavy-fermion system. On the other hand, the spin-glass-like transition appears to modify the heavy-fermion character of the specific heat. The large C/T values at low temperatures (410 mJ/mole K2 for x=0.26) probably would have been still larger if they were not reduced by the effective field of the spin-glass-like state. The low-field susceptibility measurements show spin-glass-like cusp anomalies for x=0.08, 0.15, 0.18, 0.20, 0.23, 0.34, 0.40, 0.635, 0.77, and 0.9. This anomaly in the susceptibility at Tm persists as one increases x through the antiferromagnetic percolation threshold at x≡xc ∼0.5. However, the magnitude of the susceptibility anomaly decreases two orders of magnitude as one increases x from 0.5 to 0.635. The resistivity in most respects resembles that of a dense Kondo system. It differs in that for x>xc there is an additional amomaly in the resistivity at Tm, which is absent for x≤xc. The presence of this anomaly shows that the range of the order below Tm becomes at least as long as the mean free path for x>xc. For x>xc there are two transition observed in the susceptibility, the spin-glass-like transition at Tm and an antiferromagnetic transition at low temperatures. Specific heat measurements also show the antiferromagnetic transition.