An autonomous system of ODEs which admitting a quasi-homogeneous group of symme-tries is called a quasihomogeneous one. The interest for such systems lies in the existence of particular solution in the quasi-homogeneous ray form. Yoshida[1] considered the algebraic integrability problems for quasi-homogeneous systems. Using a singularity analysis type method, he was able to derive necessary conditons for algebraic integrability. Though some imperfections in his proof was found (see [2]), Yoshida's ideas are quite fruitful and useful in this field. Inspired by Yoshida's ideas, Furta[3] made further study in this direction. He suggested a simple and easily verifiable criterion for non-existence of nontrivial analytic in-tegrals for general analytic autonomous systems. Based on his criterion, he also consider the noniategrabiltiy for general semi-quasihomogeneous systems(the definition will be given be-low). Some similar results related to nonexistence of polynomial integrals, rational integrals and analytic integrals can be found in [4]-[9].