The invention relates to a gas-tight multilayer composite tube which has a heat transfer coefficient of > 500 W/m2/K and contains at least two layers, one layer made of a nonporous monolithic oxide ceramic and one layer made of an oxide fiber composite ceramic, and relates to a connection piece containing at least one gas-conducting metal line, some regions of which overlap at least two ceramic layers in the longitudinal direction of the composite tube, wherein one ceramic layer contains a nonporous monolithic ceramic, and the other ceramic layer contains a fiber composite ceramic. The invention also relates to the use of the multilayer composite tube as a reaction tube for endothermic reactions, jet tubes, flame tubes, or rotary tubes.