In this work, we have studied noise effects in non-excitable nonlinear systems with time-delayed feedback, and in delay-coupled oscillator systems. The nonlinear systems were represented by Hopf normal forms with additive Gaussian white noise. For a single system, we performed the bifurcation and stability analysis for the deterministic equation. Then we turned on the noise and derived the stationary probability distribution for the amplitude. By changing the noise intensity, a stochastic P-bifurcation occurred for the subcritical Hopf normal form. We showed that no stochastic P-bifurcation takes place in the supercritical case.