Abstract. There are three standard ways to implicitize a rational curve or surface: resultants, Gröbner bases and Ritt-Wu's method. The resultant method can fail in the presence of base points, and Gröbner bases and Ritt-Wu's method are computationally slow. In this talk, we introduce a new method called moving curves and surfaces to implicitize a rational curve or surface. The new method can write the implicit equation in a relatively low order of determinant, and it works even in the presence of base points.