Let \(M\) be a hypersurface of an \(m\)-dimensional semi-Riemannian manifold \((\bar M, \bar g)\) of constant index \(0<\nu <m\). \(M\) is said to be a light-like hypersurface of \(\bar M\) if the normal bundle has a nontrivial intersection with the tangent bundle, i.e., the normal bundle is a subbundle of rank one of the tangent bundle over \(M\). The authors study light-like hypersurfaces for the special case when \(\bar M=\bar M(c)\) is an indefinite cosymplectic manifold of constant \(\bar\Phi\)-sectional curvature \(c\). They prove nonexistence of totally umbilical light-like hypersurfaces of indefinite cosymplectic space forms \(\bar M(c)\) with \(c\neq 0\).