Tubular bandage, in particular a finger or toe bandage which is formed as a tube comprising an outer layer which is connected to an inner layer, and wherein the outer layer has a diameter and an elasticity such that the bandage can be clamped adhesive-free around the body part to be treated, in the particular, said finger or said toe, and wherein the inner layer is made of an elastic wound-protective material, wherein said outer layer is made of an air-permeable and water-repellent material, and wherein, at the open endings, said outer layer extends in the longitudinal direction over the inner layer over a distance of more than 0.5 mm, such that the outer layer touches the body part to be treated, in particular a finger or toe, with its endings when applied.