We report on de Haas-van Alphen ͑dHvA͒ effect measurements at ambient pressure and band-structure calculations for LaRhSi 3 and CeRhSi 3 , whose crystal structures lack space-inversion symmetry. For LaRhSi 3 , dHvA frequencies up to ϳ11 kT with effective masses up to ϳ1.6m e , where m e is the free-electron mass, are observed. The observed and the calculated Fermi surfaces are in satisfactory quantitative agreement. The energy splitting of bands due to the spin-orbit coupling is estimated to be of the order of 10 2 K. For CeRhSi 3 , dHvA frequencies up to ϳ12 kT with effective masses up to ϳ19m e are observed. The dHvA frequency branches are definitely different from those observed in LaRhSi 3 and are difficult to explain with the LaRhSi 3 Fermi surface. This leads to the conclusion that the Ce 4f electrons in CeRhSi 3 are itinerant in the antiferromagnetic state at ambient pressure. The Fermi surface resulting from a band-structure calculation in which the Ce 4f electrons are treated as itinerant can provide a plausible explanation for the observed frequency branches, although the quantitative agreement is rather limited. The comparison of the calculated density of states with the Sommerfeld coefficient gives the mass enhancement factor of 8.