Self-compatible autotetraploids are likely to set much of their seed by selfing. Formulae are presented for the frequencies in any generation of states of loci, from homozygous to quadri-allelic, considering the frequencies of selfing and of double reduction but not allowing for the effects of inbreeding depression on population structure. The changing structure of populations over generations is also explored by computer simulation, incorporating selection against inbreds but ignoring double reduction. The findings are discussed in relation to mass-selection programmes.