  We investigate the $^1S_0$ neutron and proton superfluidity in isospin
asymmetric nuclear matter. We have concentrated on the isospin dependence of
the pairing gaps and the effect of a microscopic three-body force. It is found
that as the isospin asymmetry goes higher, the neutron $^1S_0$ superfluid phase
shrinks gradually to a smaller density domain, while the proton one extends
rapidly to a much wider density domain. The three-body force turns out to
weaken the neutron $^1S_0$ superfluidity slightly, but it suppresses strongly
the proton $^1S_0$ superfluidity at high densities in nuclear matter with large
isospin asymmetry.
