We discuss linear topological defects allowed in two-gap superconductors. We show that in this system there exist vortices which carry an arbitrary fraction of magnetic flux quantum. Besides that we discuss topological defects in a two-gap system which do not carry magnetic flux as well as describe features of ordinary one-magnetic flux quantum vortices in this system. We also propose an experiment where the vortices carrying a fraction of magnetic flux quantum can be created and observed. The results should be relevant for newly discovered two-band superconductor Mg B_2.