We present calculations of two-pion and two-kaon correlation functions in relativistic heavy ion collisions from a relativistic transport model that includes explicitly a first-order phase transition from a thermalized quark-gluon plasma to a hadron gas. We compare the obtained correlation radii with recent data from RHIC. The predicted R side radii agree with data while the R out and R long radii are overestimated. We also address the impact of in-medium modifications, for example, a broadening of the ρ-meson, on the correlation radii. In particular, the longitudinal correlation radius R long is reduced, improving the comparison to data. Two-particle correlations at small relative momenta have been predicted to be particularly sensitive to a phase transition from quark-gluon matter to hadronic matter [1]. For a first-order phase transition, larger hadronization times were expected to lead to considerably enhanced correlation radii, characterizing the space-time extension of the particle-emitting source, compared to, for example, a purely hadronic scenario. The radii should also depend on the critical temperature T c , the latent heat, the initial specific entropy density or the initial thermalization time of the quark-gluon phase.Here, we discuss relativistic transport calculations at RHIC energies that describe the initial dense stage by hydrodynamics [2] and the later more dilute stages by microscopic transport [3] of the particles. The two models are matched at the hadronization hypersurface [4]. In the hadronic phase the particles are allowed to rescatter and to excite resonances based on cross sections as measured in vacuum. For the initial dense (hydrodynamical) phase a bag model equation of state exhibiting a first-order phase transition is employed. Hence, a phase transition in local equilibrium that proceeds through the formation of a mixed phase, is considered. The details of this relativistic hybrid transport model can be found elsewhere [4].We first briefly summarize the main conclusions obtained in previous work [5,6,7]. Then, we show in detail the results for pions when calculating explicitly the correlation functions from the source function of the transport model. These results are subsequently compared to calculations that take in-medium modifications into account and to experimental data