Summary The observations of Ambronn on the dichroic behaviour of cellulose fibres dyed with certain direct dyes have been extended. It is found that all direct dyes, all vat dyes in the reduced leuco‐form, some insoluble azo dyes, and some acid dyes on ramie exhibit positive dichroism. Elongated direct dye micelles and dye crystals exhibit negative dichroism. These dichroic phenomena are best explained by the absorption of dye by cellulose as single molecules, not as micelles. In the dyed material the elongated direct dye molecules are oriented parallel to the cellulose molecular chains with which they are co‐ordinately combined. Direct dye molecules are positioned transversely across elongated dye micelles. These conclusions are confirmed by the dichroic behaviour of ramie dyed with alcoholic solutions of direct dyes, in which it is believed the dyes are molecularly dispersed. Normal, fully oxidised, vat dyed materials are not appreciably dichroic. A molecular theory of the dyeing of cellulose with substantive dyes is described. The dye solution is considered to contain particles of all sizes from molecules to large aggregates in a state of dynamic equilibrium. Cellulose is capable, for mechanical reasons, of absorbing molecules and small aggregates only. Further, the diffusion of dye molecules through the capillary pore system of cellulose is probably not a free diffusion, but a thermally activated process. The effect of these two factors can be combined into a “mobility factor” representing the retardation of diffusion from the speed expected for a free diffusion with absorption. The value of the mobility factor covers the range, 10‐1 to 10‐1, for the direct dye class.Dye absorption proceeds by means of the diffusion of dye molecules, which are continually re‐formed from the larger particles in dye solution, to the interior of the cellulose fibre, until finally a true equilibrium between dyed cellulose and dye solution is reached.The essential conditions necessary for substantivity of dyes on cellulose are discussed.