The critical phenomena of bistability is discussed on the basis of the relaxation equation of the nonlinear systems with a time-delayed feedback. We find that the critical slowing down at the edges of bistable region possesses consistency with the divergence of the time duration of intermittency. The critica1 exponent is 1/2. We also find that, different from the critical points at the bistable region edges, there are consistencies with the period-doubling bifurcation points and split bifurcation points at the cusp point (in cusp catastrophe model of bistability). The critical exponent is 1. The abo-ve-mentioned results possess universal properties. The computer experiments have been made in the liquid crystal hybrid optical bistable device. The results are in agreement with the analyses.