The degradation behaviour of five multilayered textured white geomembranes (GMBs) is investigated when immersed in two synthetic low-level waste (LLW) leachates with pH 7 and 9 at a range of temperatures (40–85 °C) for 48–55 months. Results are compared to the performance of the GMBs in synthetic municipal solid waste (MSW) leachate. Increasing pH from 7 to 9 gives slightly faster antioxidant depletion in LLW leachate. The estimated time to nominal failure for the GMBs is at least 20% longer in LLW leachate than in MSW leachate containing surfactant that accelerates both antioxidant depletion and stress cracking. Thus, MSW leachate can be used as a conservative proxy to estimate the service life of a GMB in contact with LLW leachate. Two GMBs are considered very highly likely to meet the required 550 year design life of the near-surface disposal facilities even based on the most conservative prediction of the time to nominal failure for the GMBs.