The invention relates to a tubular compression bandage made of a textile hosiery which is largely inelastic laterally to the longitudinal direction and is elastic in the longitudinal direction, and which is adapted in tubular form to the contours of the limb in such a way that, when the bandage is applied, it snugly surrounds the limb, the bandage being divided by at least one closure running in the longitudinal direction, such that, when the closure is open, the bandage is applicable to the limb, and when the closure is closed, the bandage firmly surrounds the limb. The bandage material is designed by an elastic, porous knitted fabric having incorporated, circumferential inelastic tension threads for forming a lateral inelasticity, while maintaining the longitudinal elasticity, and the bandage is provided with a window which is held closed or completely or partially open by a textile cover which is made of longitudinally and laterally elastic material and is adapted to the window.