The relative biological effectiveness (RBE) for animal tumors treated with fractionated doses of 290 MeV/u carbon ions was studied. The growth delay of NFSa fibrosarcoma in mice was investigated following various daily doses given with carbon ions or those given with cesium gamma-rays, and the RBE was determined. Animal tumors were irradiated with carbon ions of various LET (linear energy transfer) in a 6-cm SOBP (spread-out Bragg peak), and the isoeffect doses; i.e. the dose necessary to induce a tumor growth delay of 15 days were studied. The iso-effect dose for carbon ions of 14 and 20 keV/microm increased with an increase in the number of fractions up to 4 fractions. The increase in the isoeffect dose with the fraction number was small for carbon ions of 44 keV/microm, and was not observed for 74 keV/microm. The alpha and beta values of the linear-quadratic model for the radiation dose-cell survival relationship were calculated by the Fe-plot analysis method. The alpha values increased linearly with an increase in the LET, while the beta values were independent of the LET. The alpha/beta ratio was 129 +/- 10 Gy for gamma-rays, and increased with an increase in the LET, reaching 475 +/- 168 Gy for 74 keV/microm carbon ions. The RBE for carbon ions relative to Cs-137 gamma-rays increased with the LET. The RBE values for 14 and 20 keV/microm carbon ions were 1.4 and independent of the number of fractions, while those for 44 and 74 keV/microm increased from 1.8 to 2.3 and from 2.4 to 3.0, respectively, when the number of fractions increased from 1 to 4. Increasing the number of fractions further from 4 to 6 was not associated with an increase in the RBE. These results together with our earlier study on the skin reaction support the use of an RBE of 3.0 in clinical trials of 80 keV/microm carbon beams. The RBE values for low doses of carbon beams were also considered.