A process for reshaping keratin fibers, preferably human keratin fibers, more preferably human hair characterized in that it comprises the steps of: a) putting keratin fibers under mechanical tension, b) applying to keratin fibers a non-reducing, non-oxidizing alkaline composition with a pH in the range of 7 to 12, preferably in the range of 8 to 11, comprising: i) one or more alkalizing agent(s), ii) one or more thickening polymer(s), iii) one or more organic solvent(s) having two or more hydroxyl groups, c) optionally covering keratin fibers with a moisture barrier, d) heating the keratin fibers to a temperature in the range of 50°C to 230°C, e) optionally removing the moisture barrier from keratin fibers, f) releasing tension from keratin fibers, g) optionally rinsing-off the keratin fibers, wherein process steps a), b), and f), g) can be executed in either order, and wherein the following non-reducing, non-oxidizing alkaline compositions are excluded from step b) Ex. 1 Ex. 2 Comp. Ex. 2 Comp. Ex. 3 Comp. Ex. 4 KOH 6.8 6.8 6.8 6.8 6.8 Taurine 15.4 15.4 15.4 15.4 15.4 Butylene Glycol 10 - - - - Pentylene Glycol - 10 - - - Glycerin - - 10 - - Propylene Glycol - - - 10 - Hexylene Glycol - - - - 10 Hydroxyethylcellulose 1.5 1.5 1.5 1.5 1.5 Polyquaternium-67 0.5 0.5 0.5 0.5 0.5 Dimethicone 0.2 0.2 0.2 0.2 0.2 Water qsp 100 qsp 100 qsp 100 qsp 100 qsp 100 pH 10.7 10.7 10.7 10.7 10.7 and Ex. 3 Ex. 4 Ex. 5 NaOH 2.4 2.4 2.4 Monoethanolamine 3.6 3.6 3.6 Taurine 8.7 8.7 8.7 Magnesium Gluconate 0.125 0.125 0.125 Pentylene Glycol 10 7.5 5 Ethanol - 2.5 5 Hydroxyethylcellulose 1.5 1.5 1.5 Polyquaternium-67 0.5 0.5 0.5 Dimethicone 0.2 0.2 0.2 Mineral Oil 5 5 5 Steareth-2 2 2 2 Steareth-20 2 2 2 Water qsp 100 qsp 100 qsp 100 pH 10.7 10.7 10.7 a) putting keratin fibers under mechanical tension, b) applying to keratin fibers a non-reducing, non-oxidizing alkaline composition with a pH in the range of 7 to 12, preferably in the range of 8 to 11, comprising: i) one or more alkalizing agent(s), ii) one or more thickening polymer(s), iii) one or more organic solvent(s) having two or more hydroxyl groups, i) one or more alkalizing agent(s), ii) one or more thickening polymer(s), iii) one or more organic solvent(s) having two or more hydroxyl groups, c) optionally covering keratin fibers with a moisture barrier, d) heating the keratin fibers to a temperature in the range of 50°C to 230°C, e) optionally removing the moisture barrier from keratin fibers, f) releasing tension from keratin fibers, g) optionally rinsing-off the keratin fibers, wherein process steps a), b), and f), g) can be executed in either order, and wherein the following non-reducing, non-oxidizing alkaline compositions are excluded from step b) Ex. 1 Ex. 2 Comp. Ex. 2 Comp. Ex. 3 Comp. Ex. 4 KOH 6.8 6.8 6.8 6.8 6.8 Taurine 15.4 15.4 15.4 15.4 15.4 Butylene Glycol 10 - - - - Pentylene Glycol - 10 - - - Glycerin - - 10 - - Propylene Glycol - - - 10 - Hexylene Glycol - - - - 10 Hydroxyethylcellulose 1.5 1.5 1.5 1.5 1.5 Polyquaternium-67 0.5 0.5 0.5 0.5 0.5 Dimethicone 0.2 0.2 0.2 0.2 0.2 Water qsp 100 qsp 100 qsp 100 qsp 100 qsp 100 pH 10.7 10.7 10.7 10.7 10.7 and Ex. 3 Ex. 4 Ex. 5 NaOH 2.4 2.4 2.4 Monoethanolamine 3.6 3.6 3.6 Taurine 8.7 8.7 8.7 Magnesium Gluconate 0.125 0.125 0.125 Pentylene Glycol 10 7.5 5 Ethanol - 2.5 5 Hydroxyethylcellulose 1.5 1.5 1.5 Polyquaternium-67 0.5 0.5 0.5 Dimethicone 0.2 0.2 0.2 Mineral Oil 5 5 5 Steareth-2 2 2 2 Steareth-20 2 2 2 Water qsp 100 qsp 100 qsp 100 pH 10.7 10.7 10.7 wherein process steps a), b), and f), g) can be executed in either order, and wherein the following non-reducing, non-oxidizing alkaline compositions are excluded from step b) Ex. 1 Ex. 2 Comp. Ex. 2 Comp. Ex. 3 Comp. Ex. 4 KOH 6.8 6.8 6.8 6.8 6.8 Taurine 15.4 15.4 15.4 15.4 15.4 Butylene Glycol 10 - - - - Pentylene Glycol - 10 - - - Glycerin - - 10 - - Propylene Glycol - - - 10 - Hexylene Glycol - - - - 10 Hydroxyethylcellulose 1.5 1.5 1.5 1.5 1.5 Polyquaternium-67 0.5 0.5 0.5 0.5 0.5 Dimethicone 0.2 0.2 0.2 0.2 0.2 Water qsp 100 qsp 100 qsp 100 qsp 100 qsp 100 pH 10.7 10.7 10.7 10.7 10.7 and Ex. 3 Ex. 4 Ex. 5 NaOH 2.4 2.4 2.4 Monoethanolamine 3.6 3.6 3.6 Taurine 8.7 8.7 8.7 Magnesium Gluconate 0.125 0.125 0.125 Pentylene Glycol 10 7.5 5 Ethanol - 2.5 5 Hydroxyethylcellulose 1.5 1.5 1.5 Polyquaternium-67 0.5 0.5 0.5 Dimethicone 0.2 0.2 0.2 Mineral Oil 5 5 5 Steareth-2 2 2 2 Steareth-20 2 2 2 Water qsp 100 qsp 100 qsp 100 pH 10.7 10.7 10.7