Permeation of carbon dioxide has been measured for two types of composite polymeric hollow fiber membranes for feed pressures up to 18MPa at a temperature of 313K. The membranes consist of a polyamide copolymer (IPC) layer or a polyvinyl alcohol (PVA) layer on top of a polyethersulfone (PES) support membrane. For both membranes, the carbon dioxide permeance has a maximum as a function of the feed pressure at about 8MPa. A good description of the maximum in the carbon dioxide permeance is possible with a model based on the ratio of the density to viscosity. A comparison with permeation results for nitrogen for feed pressures up to 16MPa, supports the findings that viscous flow is the main mechanism for mass transport across the membranes. Both membranes show an increase in the carbon dioxide permeance as a function of the exposure time to supercritical carbon dioxide. Cross-linking of the IPC layer resulted in a stable IPC-based membrane at the cost of a small reduction in the carbon dioxide permeance.