The properties of certain recently proposed topological vortices which can occur at either grand-unification or intermediate energy scales are examined. These vortices are topologically stable in that they survive any subsequent symmetry breakings. We find them also to be dynamically stable because some of their quantum numbers have fractional values. Zero-energy bound states with certain fermions are found and these states are seen to transform like SU(5) families and mirror families. We also comment on the analog of the Rubakov-Callan effect for the above vortices. © 1984 The American Physical Society.