Pion and kaon correlations in relativistic nuclear collisions are studied in the framework of boost-invariant, cylindrically symmetric hydrodynamics. It is investigated how the inverse widths, R out , R side , of the two-particle correlation functions in out-and side-direction depend on the average transverse momentum K ⊥ of the particle pair, the initial energy density ǫ 0 , and the equation of state of the system. The QCD transition leads to a time delay in the expansion of the system and consequently to an enhancement of the ratio R out /R side . This time-delay signal is found to be particularly strong for large average transverse momenta K ⊥ ∼ 1 GeV and initial energy densities accessible at RHIC, ǫ 0 ∼ 10 − 20 GeV fm −3 . Neutral kaon pair correlation functions, which are not influenced by final state Coulomb effects and less contaminated by resonance decays than pion correlation functions, seem to be the ideal tool to detect this collective time-delay signature of the QCD transition. † Supported by DFG, BMBF, GSI, and DOE.