We discuss the evolution of the mixed phase at RHIC and SPS within boost-invariant hydrodynamics. In addition to the hydrodynamical expansion, we also consider evaporation of particles off the surface of the fluid. The back reaction of this evaporation process on the dynamics of the fluid shortens the lifetime of the mixed phase. In our model this lifetime of the mixed phase is less than or equal to 12 fm/c in Au+Au at RHIC and less than or equal to 8 fm/c in Pb+Pb at SPS, even in the limit of vanishing transverse expansion velocity. Strong separation of strangeness occurs. especially in events (or at rapidities) with relatively high initial net baryon and strangeness number, enhancing the multiplicity of multiply strange nuclear clusters. If antiquarks and antibaryons reach saturation in the course of the pure QGP or mixed phase, we find that at RHIC the ratio of antideuterons to deuterons may exceed 0.3 and even He-4 /He-4>0.1. In S+Au at SPS we find only N/N approximate to 0.1. As a result of fluctuations, at RHIC even a negative baryon number at midrapidity is possible in individual events, so that the antibaryon and antibaryon-cluster yields exceed those of the corresponding baryons and clusters.