An oxidation composition for oxidative hair treatment, containing - 50-96 wt.%, preferably 70-93 wt.%, particularly preferably 80-90 wt.%, water, - 0.5-20 wt.% hydrogen peroxide, - at least one linear saturated 1-alkanol having 12-30 carbon atoms, preferably in a total amount of 2-8 wt.%, particularly preferably 3 to 6.5 wt.%, - at least one glyceryl fatty acid ester of general formula, in which - R1, R2 and R3 represent, independently of one another, a hydrogen atom or a grouping of formula, in which - R4 represents an unbranched or branched, saturated or unsaturated C 11 -C 27 alkyl group, - with the proviso that at least one and at most two of the functional groups selected from R1, R2 and R3 represent a grouping of formula, the at least one glyceryl fatty acid ester of general formula being contained preferably in a total amount of 0.01-1 wt.%, particularly preferably 0.1 to 0.8 wt.%, - at least one ethoxylated fatty alcohol of formula in which R5 represents a saturated or unsaturated, unbranched or branched C 8 -C 24 alkyl group, preferably a saturated, unbranched C 16 or C 18 alkyl group, and n represents an integer from 10 to 30, preferably an integer from 12 to 25, more preferably an integer from 15 to 20, the at least one ethoxylated fatty alcohol of formula being contained preferably in a total amount of 0.25-2 wt.%, particularly preferably 0.5 to 1.5 wt.%, - at least one ethoxylated fatty alcohol of formula in which R5 represents a saturated or unsaturated, unbranched or branched C 8 -C 24 alkyl group, preferably a saturated, unbranched C 16 or C 18 alkyl group, and n represents an integer from 50 to 150, preferably an integer from 80 to 120, more preferably the number 100, the at least one ethoxylated fatty alcohol of formula being contained preferably in a total amount of 0.03-0.3 wt.%, particularly preferably 0.08 to 0.25 wt.%, extremely preferably 0.1-0.2 wt.%, - at least one polyol selected from C 2 -C 9 alkanols having 2-6 hydroxyl groups and polyethylene glycols having 3-20 ethylene oxide units and mixtures thereof, preferably in a total amount of 1-10 wt.%, particularly preferably 2-8 wt.%, extremely preferably 3-6 wt.%, and - at least one oil, preferably in a total amount of 0.1-5 wt.%, particularly preferably 0.2 to 3 wt.%, extremely preferably 0.5 to 2.5 wt.%, all stated amounts being based on the weight of the oxidation composition, characterized in that at least one lamellar phase is contained. - 50-96 wt.%, preferably 70-93 wt.%, particularly preferably 80-90 wt.%, water, - 0.5-20 wt.% hydrogen peroxide, - at least one linear saturated 1-alkanol having 12-30 carbon atoms, preferably in a total amount of 2-8 wt.%, particularly preferably 3 to 6.5 wt.%, - at least one glyceryl fatty acid ester of general formula, in which - R1, R2 and R3 represent, independently of one another, a hydrogen atom or a grouping of formula, in which - R4 represents an unbranched or branched, saturated or unsaturated C 11 -C 27 alkyl group, - with the proviso that at least one and at most two of the functional groups selected from R1, R2 and R3 represent a grouping of formula, the at least one glyceryl fatty acid ester of general formula being contained preferably in a total amount of 0.01-1 wt.%, particularly preferably 0.1 to 0.8 wt.%, - at least one ethoxylated fatty alcohol of formula in which R5 represents a saturated or unsaturated, unbranched or branched C 8 -C 24 alkyl group, preferably a saturated, unbranched C 16 or C 18 alkyl group, and n represents an integer from 10 to 30, preferably an integer from 12 to 25, more preferably an integer from 15 to 20, the at least one ethoxylated fatty alcohol of formula being contained preferably in a total amount of 0.25-2 wt.%, particularly preferably 0.5 to 1.5 wt.%, - at least one ethoxylated fatty alcohol of formula in which R5 represents a saturated or unsaturated, unbranched or branched C 8 -C 24 alkyl group, preferably a saturated, unbranched C 16 or C 18 alkyl group, and n represents an integer from 50 to 150, preferably an integer from 80 to 120, more preferably the number 100, the at least one ethoxylated fatty alcohol of formula being contained preferably in a total amount of 0.03-0.3 wt.%, particularly preferably 0.08 to 0.25 wt.%, extremely preferably 0.1-0.2 wt.%, - at least one polyol selected from C 2 -C 9 alkanols having 2-6 hydroxyl groups and polyethylene glycols having 3-20 ethylene oxide units and mixtures thereof, preferably in a total amount of 1-10 wt.%, particularly preferably 2-8 wt.%, extremely preferably 3-6 wt.%, and - at least one oil, preferably in a total amount of 0.1-5 wt.%, particularly preferably 0.2 to 3 wt.%, extremely preferably 0.5 to 2.5 wt.%,