Curvature properties of some generalizations of contact metric manifolds are studied. In particular, some results on so-called almost \(S\)-manifolds are obtained. The main result is the following: Theorem. Let \(Z= (M^{2n+s},\varphi, \xi, \eta,g)\) be an almost \(S\)-manifold and \((\widetilde\varphi, \widetilde\xi, \widetilde\eta, \widetilde g)\) an almost \(S\)-structure on \(M\) obtained by a \({\mathcal D}\)-homothetic, transformation of constant \(a\). If \(Z\) verifies the \((\kappa,\mu)\)-nullity condition for certain real constants \((\kappa,\mu)\), then \((M,\widetilde\varphi, \widetilde\xi, \widetilde\eta,\widetilde g)\) verifies the \((\widetilde\kappa, \widetilde\mu)\)-nullity condition, where \[ \widetilde\kappa= {\kappa+ a^2-1\over a^2},\qquad \widetilde\mu= {\mu+ 2(a- 1)\over a}. \]