The nonlinear differential system x_ =P`i=0 Pmi (x; y); y_ = P`i=0 Qmi (x; y) is considered, where Pmi and Qmi are homogeneous polynomials of degree mi ¸ 1 in x and y, m0 = 1. The set f1;mig`i=1 consists of a finite number (l < 1) of distinct integer numbers. It is shown that the maximal number of algebraically independent focal quantities that take part in solving the center-focus problem for the given differential system with m0 = 1, having at the origin of coordinates a singular point of the second type (center or focus), does not exceed % = 2( P`i=1mi `) 3: We make an assumption that the number ! of essential conditions for center which solve the center-focus problem for this differential system does not exceed %, i. e. ! · %.