  We present two types of models for hybrid compact stars composed of a quark
core and a hadronic mantle with an abrupt first order phase transition at the
interface which are in accordance with the latest astrophysical measurements of
two 2 M_sun pulsars. While the first is a schematic one, the second one is
based on a QCD motivated nonlocal PNJL model with density-dependent vector
coupling strength. Both models support the possibility of so called twin
compact stars which have the same mass but different radius and internal
structure at high mass (~2 M_sun), provided they exhibit a large jump \Delta
\epsilon in the energy density of the first order phase transition fulfilling
\Delta \epsilon/\epsilon_crit > 0.6. We conclude that the measurement of
high-mass twin stars would support the existence of a first order phase
transition in symmetric matter at zero temperature entailing the existence of a
critical end point in the QCD phase diagram.
