||Magnetic, transport, and thermal properties of CeCu2Mg are investigated to elucidate the lack of magnetic order in this heavy-fermion compound with a specific heat value, Cmag/T|Tâ†’0â‰ˆ1.2 J/mol K2 and robust effective magnetic moments (Î¼effâ‰ˆ2.46Î¼B). The lack of magnetic order is attributed to magnetic frustration favored by the hexagonal configuration of the Ce sublattice. In fact, the effect of magnetic field on Cmag/T and residual resistivity Ï0 does not correspond to that of a Fermi liquid (FL) because a broad anomaly appears at Tmaxâ‰ˆ1.2 K in Cmag(T)/T, without changing its position up to Î¼0H=7.5 T. However, the flattening of Cmag/T|Tâ†’0 and its magnetic susceptibility Ï‡Tâ†’0, together with the T2 dependence of Ï(T), reveal a FL behavior for Tâ‰¤2 K which is also supported by Wilson and Kadowaki-Woods ratios. The unusual coexistence of FL and frustration phenomena can be understood by placing paramagnetic CeCu2Mg in an intermediate section of a frustration-Kondo model. The entropy, Smag, reaches 0.87Rln6 at Tâ‰ƒ100 K, with a tendency to approach the expected value Smag=Rln6 of the J=5/2 ground state of Ce3+.