Consider the differential systemformulawhere P4 , Q4 are homogeneous polynomial of degree 4. Denote by E the space of coefficients of system (1) and by GL(2, R) the group of center-affine transformations of the phase space xOy . There is a biunivoc correspondence between E and system (1). Consider a the point from E what corresponding to (1), and a(q) the point from E , what corresponding to differential system obtained from (1), after the transformation of the variables (x, y)Tr →q ⋅ (x, y)Tr . The set O(a) = {a(q) | q∈GL(2, R)}⊂ E is called the GL(2, R) -orbit of the point a∈ E or of the differential system (1) corresponding to this point. In the space E any GL(2, R) -orbits is a 4-parameter surface. The dimension of the tangent space to O(a) at the point a is called the dimension of that orbit. An orbit can has the dimension equal to 0; 1; 2; 3 or 4. Theorem. The right-hand sides of any system (1) with the GL(2, R) -orbit of dimension less than four have common divisor of degree not less than 3.