  We present a compared analysis of some properties of indefinite almost
$\mathcal{S}$-manifolds and indefinite $\mathcal{S}$-manifolds. We give some
characterizations in terms of the Levi-Civita connection and of the
characteristic vector fields. We study the sectional and ${\phi}$-sectional
curvature of indefinite almost $\mathcal{S}$-manifolds and state an expression
of the curvature tensor field for the indefinite $\mathcal{S}$-space forms. We
analyse the sectional curvature of indefinite $\mathcal{S}$-manifold in which
the number of the spacelike characteristic vector fields is equal to that of
the timelike characteristic vector fields. Some examples are also described.
