New associative thickeners of the HEUR type (Hydrophobically modified Ethylene oxide URethane) whose hydrophobic monomer is based on alkyl cyclohexylols. These are new polyurethanes that allow a broad thickening of a medium shear gradient aqueous formulation while limiting the increase in the low shear gradient viscosity. The invention also concerns the compositions containing them and their uses in different formulations such as aqueous paints.