Abstract: The objective of this paper is to present some criteria for nonexistence and partial existence of rational first integrals for general nonlinear systems. The author first gives a necessary condition for general nonlinear systems to having rational first integrals. Then the author considers the case that the system have owed some rational integrals. Under certain conditions, the author proves that the system does not admit any other rational first integrals in the sense of functional independence, and thus the system is partially integrable.

Key words: Nonlinear systems, First integrals, Nonintegrable, Partially integrable