The authors are concerned with the existence of global, smooth first integrals of noncritical, autonomous first order systems of ordinary differential equation in the plane of such kind: (1) \(x'= f(x)\), \(x\in R^ 2\), \(f\in C^ k(R^ 2,R^ 2)\), \(1\leq k\leq \omega\). It is proved that, if the system from (1) is of class \(C^ k\) and the limit separatrices do not accumulate, then there exists a global first integral of class \(C^ k\) \((k\neq \omega)\).