An excellent oil-thickening or -gelling agent is provided. The agent is compatible with various oils and can freely control the form or viscosity of oily raw materials or cosmetics by changing the quantity thereof added. The agent contains a novel co-modified organopolysiloxane that contains both a group having a siloxane dendron structure and a hydrophilic group and that preferably has a degree of polymerization of 200 or more. A gel composition containing the co-modified organopolysiloxane is also provided. The gel composition is useful as a base that permits stable and easy preparation of cosmetics having various viscoelasticities and forms. An oil is kept in the form of a gel that has a viscoelasticity falling within the intermediate range between the viscoelasticity of liquid and that of solid. Cosmetics containing the thickening or gelling agent are also provided.