1. Inactivation of one X chromosome in somatic cells of female mammals is a form of dosage compensation of sex-linked genes, but the mechanism is entirely different from that operating in Drosophila. The latter is designated as dosage compensation sensu strictu.2. There is no dosage compensation of barred, sex-linked dilution or slow-feathering in domestic fowls, of almond or faded in pigeons, or of cinnamon in canaries. Among Lepidoptera the same is true of sex-linked melanism in Lymantria monacha and of a locus controlling haemolymph colour in Choritoneura spp. There is no positive evidence that dosage compensation occurs outside Drosophila and mammals.3. Sex-chromatin in female birds (heterogametic) has been reported by several authors; the genetical evidence is against the possibility that this represents (as in mammals) an inactivated X chromosome. Sex-chromatin in the heterogametic sex also occurs in some (not all) Lepidoptera and Heteroptera; in Heteroptera it usually represents a heteropyknotic Y chromosome.4. Some complications in Muller's theory of dosage compensation sensu strictu are discussed. Not all ‘compensatory modifiers’ are necessarily sex-linked.5. The problem of dosage compensation in species with impaternate males is discussed; fused in Habrobracon is not compensated.