This paper investigates the computation of the simple bifurcation points, the double bifurcation points and the Hopf bifurcation points for diffusion-reaction equations discretized with orthogonal collocation. Both the direct and indirect methods are used. The test problems selected are well-known diffusion-reaction equations (catalyst pellet and 2-D thermal explosion). the results show that orthogonal collocation can be used successfully in solving bifurcation problems.