We have synthesized the Ce1-xLaxB2C2 and Ce1-xLuxB2C2 samples and measured the temperature dependence of low-field magnetization, AC-susceptibility and specific heat. As the La or Lu concentration x increases, the Neel temperature T-N decreases linearly for x <= 0.20. However, concentration x dependence of the transition temperature changes the slope at x similar to 0.25; and spin-glass transitions are observed for x >= 0.25. The origin of the spin-glass behavior will be discussed. (C) 2003 Elsevier B. V. All rights reserved.