A shaft seal for sealing a gap between a shaft and a casing is provided. The shaft seal includes a plurality of sealing modules, at least one fluid supply and one fluid drain, and a first main seal on which a major partial pressure difference occurs. Conventional shaft seals of the above type require significant amounts of additional barrier fluid in regular intervals to ensure suitable pressure gradients. In the presently proposed shaft seal, the first main seal is designed as a radial double seal which is defined by two gas seals having respective rotating sealing surfaces and stationary sealing surfaces, the pair of sealing surfaces being opposite each other in a respective sealing plane. The sealing planes extend in a substantially radial manner relative to the shaft.