||Due to the proximity of CeCu2Si2 to a quantum critical point, the ground state of this compound is extremely sensitive to sample preparation conditions. Small excess of one component can lead to magnetic or superconducting behaviors. We found that in the alloy CeCu2(Si1-xGex)(2) a small excess of Ge enhances the homogeneity range allowing a precise investigation of stoichiometric effects on the physical properties. In this system, Ge doping produces an increment of the antiferromagnetic transition temperature T-N, while the superconducting one decreases. Particularly, it was found that at x = 0.1 both phases coexist at low temperature. In order to investigate the stability of these phases against changes of the Ce-ligands composition, we prepared a series of CeCu2+y(Si0.9Ge0.1)2-x, samples (0less than or equal toyless than or equal to0.10) and investigated their specific heat and electrical resistivity. We observed that the substitution of Si/Ge by Cu increases the characteristic temperature and weakens the magnetic contribution without modifying TN. A further transition, of the first order character, is observed at lower temperature. (C) 2002 Elsevier Science B.V. All rights reserved.