Summary: Virial identities for nonlinear Schrödinger equations with some strongly singular potential \((a|x|^{-2})\) are established. Here if \(a=a(N) := -(N-2)^2/4\), then \(P_{a(N)}:=-\Delta+a(N)|x|^{-2}\) is nonnegative selfadjoint in the sense of Friedrichs extension. But the energy class \(D((1 + P_{a(N)})^{1/2})\) does not coincide with \(H^1(\mathbb{R}^{N})\). Thus justification of the virial identities has a lot of difficulties. The identities can be applicable for showing blow-up in finite time and for proving the existence of scattering states.