  We investigate superfluidity in the interior-gap states proposed by Liu and
Wilczek. At weak coupling, we find the {\em gapless} interior-gap state
unstable in physically accessible regimes of the parameter space, where the
superfluid density is shown to be always negative. We therefore conclude that
the spatially-uniform interior-gap phase is extremely unstable unless it is
fully gapped; in this case, however, the state is rather similar to
conventional BCS states.
