On some systems of non-algebraic equations in $\mathbb C^n$

A method of finding residue integrals for systems of non-algebraic equations containing entire functions is presented in the paper. Such integrals are connected with the power sums of roots of certain system of equations. The proposed approach can be used for developing methods for the elimination of unknowns from systems of non-algebraic equations. It is shown that obtained results can be used for investigation some model of chemical kinetics.