Abstract: Cellulosic textile material is dyed with substantive dyes or preferably with reactive dyes. Dyeing is carried out by applying to the cellulosic material, by a non-pad method, an aqueous dye liquor which contains, in addition to the dye, a graft polymer which is obtained from an adduct of an alkylene oxide, preferably propylene oxide, with an at least trihydric aliphatic alcohol, e.g. glycerol, and acrylamide or methacrylamide. The cellulosic material is then subjected to a heat treatment, e.g. by steaming or with microwaves, or is preferably stored cold, to fix the dyes.This dyeing process affords dyeings with excellent penetration of the fabric and with level depth of shade from edge to edge.