The present invention describes a one-part moisture-curing liquid-applied waterproofing membrane including a polyurethane polymer and both an aldimine and an oxazolidine as blocked amine hardeners in a specific ratio range. The membrane has a low odor, a long shelf life stability, a low viscosity at low solvent content, a sufficiently long open time to allow hand application and cures fast to a solid elastic material. The liquid-applied waterproofing membrane can be suitable for roofing applications, possessing high strength, high elongation and good durability under outdoor weathering conditions in a broad temperature range.