Ideal theoretic complete intersections in ${\bf P}\sp 3\sb K$

We describe the monomial curves in $P_K^3$ ($K$ algebraically closed field of characteristic zero) that are set theoretical complete intersections on two binomial surfaces. We prove that they are exactly those which are ideal theoretic complete intersections. Using that, we get explicitly all monomial curves that are ideal theoretic complete intersections and a minimal generating basis for their ideals.