Carbon Capture and Storage (CCS) is becoming a widely used technology to achieve the climate goals and reduce atmospheric carbon-dioxide contents and achieve net CO2 neutrality. Over the past decade there have been an increasing number of studies on storing carbon-dioxide in saline aquifers. While reservoir properties have been well studied, less is known about caprock integrity and permeability. Therefore, we carried out permeability measurements on low-permeable rocks, as it is one of most important physical properties determining the quality of both reservoir- and caprocks. Permeability was measured using Helium, with corrections made for gas slippage using the Klinkenberg-correction on shales, claystones, and evaporites. In our measurements we noticed the effect of increased confining pressure over time, highlighting the stress equilibration of cap rocks has to be considered. For the comparative study we measured permeability of select cap rocks at a constant isostatic confining stress of 300 bar (30 MPa) over a period of 5 to 7 days to show that repeatable measurements of cap rock permeability at subsurface stress conditions require an equilibration period. This equilibration period is a function of the rocks mineralogy and texture. The results suggest, samples, which contain abundant ductile clay minerals, should be kept under elevated confining stresses for at least for 3 days to obtain reliable permeability data. Evaporite samples have been shown to be less sensitive to elevated confining stresses and show an equilibration of repeatable permeability measurements after 1,5 days.