Аннотация:We consider autonomous planar systems of ordinary differential equations with a polynomial
nonlinearity. These systems are resolved with respect to derivatives and can contain free
parameters. To study local integrability of the system near each stationary points, we use
an approach based on Power Geometry and on the computation of the resonant normal
form. For the pair of concrete planar systems, we found the complete set of necessary conditions on parameters of the system for which the system is locally integrable
near each stationary points. The main idea of this report is in the hypothesis that if for the fixed set of parameters, such that at all stationary points of the system this system is locally integrable then this system has the global first integral of motion. So from some finite set of local properties, we can obtain a global property. But if the system has some invariant lines or separatists, this first integral can exist only in the part of the phase space, where the local integrable points take place.