  We analyze the different possibilities for the hadron-quark phase transition
occurring in beta-stable matter including hyperons in neutron stars. We use a
Brueckner-Hartree-Fock approach including hyperons for the hadronic equation of
state and a generalized MIT bag model for the quark part. We then point out in
detail the differences between Maxwell and Gibbs phase transition constructions
including the effects of surface tension and electromagnetic screening. We find
only a small influence on the maximum neutron star mass, whereas the radius of
the star and in particular its internal structure are more affected.
