The Constrained Delaunay Triangulation of a set of obstacle line segments in the plane is the Delaunay triangulation of the endpoint set of these obstacles with the restriction that the edges set of the triangulation contains all these obstacles. In this paper we present an optimal \(\Theta(\log n + k)\) algorithm for inserting an obstacle line segment or deleting an obstacle edge in the constrained Delaunay triangulation of a set of \(n\) obstacle line segments in the plane. Here \(k\) is the number of Delaunay edges deleted and added in the triangulation during the updates.