Abstract: This paper discusses the coincidence condition of two Bezier curves of the same degree, which is necessary for a curve/curve intersection algorithm. It proves that two Bezier curves of the same degree are coincident with each other if and only if they have a coincident control polygon or they can be reparameterized into the same non-reparameterizable Bezier curve of a lower degree. A simple method is also provided for detecting the reparameterizable case where a Bezier curve can be reparameterized into a non-reparameterizable one of a lower degree.