  We discuss the Skyrme model for strong interactions and the concept of a
Skyrmion fluid. The corresponding compact objects, namely Skyrmion stars,
constructed from the equation of state describing such a fluid are presented
and compared to models of neutron stars based on modern equation of states. We
suggest plausible Skyrmion star candidates in the 4U 1636-53 and 4U 1820-30 low
mass X-ray binary systems where the suggested masses of the accreting compact
companion (\sim 2.0M_{\odot}) remain a challenge for neutron star models.
