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Ternary intermetallic alloys Ce2Rh3+xGe1-x (0 ≤ x ≤ 0.33) crystallize with a rhombohedral structure of the Mg2Ni3Si-type [derivative of the MgCu2-type Laves phase, space group R-3m (No. 166), Pearson symbol hR18, Z = 3, 6Ce at 6c, 9Rh at 9d, mixture of 3[(1-x)Ge + xRh] (0 ≤ x ≤ 0.33) atoms at 3a]. With varying the stoichiometry, the lattice parameters notably change from a = 5.5887(2) Å, c = 11.9557(5) Å (hexagonal setting) for Ce33.3Rh50.0Ge16.7 (x = 0) to a = 5.5127(2) Å, c = 12.2790(5) Å for Ce33.3Rh55.6Ge11.1 (x = 0.33), while the unit cell volume remains nearly same. Ce2Rh3+xGe1-x alloys show thermodynamic and electrical transport properties characteristic of intermediate-valent systems with nonmagnetic 4f0 configuration of the electronic ground state of Ce ions. With changing the composition, the energy scale of spin fluctuations diminishes from about 660 K in Ce33.3Rh50.0Ge16.7 to about 540 K in Ce33.3Rh55.6Ge11.1. Both alloys exhibit metallic conductivity and slightly enhanced electronic contribution to the specific heat of about 25 mJ/(mol K2) per Ce atom.