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The physical properties of two novel Ce-based intermetallics Ce3RhSi3 and Ce3IrSi3 have been studied by means of magnetization, electrical resistivity and heat capacity measurements, performed down to 350 mK in magnetic fields up to 9 T. The compounds crystallize with an orthorhombic structure of the Y3NiSi3 type (space group Immm) that can be considered as a combination of AlB2- and W-type units. There are two inequivalent sites for Ce atoms in the unit cell and both are occupied by trivalent ions, as inferred from a Curie-Weiss analysis of the magnetic susceptibility. The magnetic and electrical transport data distinctly manifest Kondo interactions with the characteristic temperature scale of about 6-10 K. Nevertheless, the two compounds order ferromagnetically at low temperatures, namely at TC = 4.4 K for Ce3RhSi3 and TC = 10.5 K for Ce3IrSi3. Moreover, the latter silicide undergoes a ferromagnetic-like order-order transition at Tt = 3 K. In the ordered state, the electrical resistivity and the specific heat of both ternaries are governed by ferromagnetic spin-waves contribution. In turn, their low-temperature specific heat shows a large enhancement [C/T = 700 and 460 mJ/(mol K2) for the Rh- and Ir-containing phase, respectively], thus implying the formation of heavy-electron ground states.