A population genetic model is proposed for the reproduction of self-incompatible inbred lines in which incompatibility is controlled by 1-4 loci. From theoretical considerations it was expected that: a) with the random matings of lines In, (obtained by self-pollination of n generations), some lines would be cross-incompatible (all the plants within these lines would be homozygous for S-genes) and the rest would be cross-compatible (retain heterozygosity for one or more S-genes); b) in the case of random matings of Unes InGm (obtained by self-pollination of n generations and by random pollination for m generations), some lines would be cross-incompatible (heterozygous for one S-gene) and the rest would be cross-compatible (retain heterozygosity for two or more S-genes); c) the relative proportion of sterile plants, obtained by random pollination of cross-compatible lines, would be related to the number of segregating S-loci and to the generation in which the lines are studied.Forty-four inbred lines of sugar beet derived from self-incompatible plants of a population were analysed. Comparisons of the observed values with the theoretically expected ones demonstrated that: a) of 18 In (I1-I4) lines, 6 were cross-incompatible (homozygous for S-genes) and 12 were cross-compatible having one S-locus segregating in 7 lines and two S-loci segregating in 5 lines; b) of 22 InG1 (I2G1 and I3G1) lines, one line was self-fertile, 7 lines were cross-incompatible (heterozygous for one S-loci) and 14 lines were cross-compatible (heterozygous for two S-loci).No line was found to have three or more segregating S-loci. The results of this population genetics analysis of self- and cross-incompatibility in sugar beet comply with diallel analysis data on sugar beet incompatibility and indicates that it is under the gametophytic control of two basic S-loci.