On systems of linear functional equations of the third kind in $L_2$

We consider the systems of linear functional equations of the third kind with measurecompact operators in $L_2$ and the general systems of linear integral equations of the third kind in $L_2$. We propose a method for reducing these systems either to equivalent integral equations of the first kind with nuclear operators or to equivalent integral equations of the second kind with quasidegenerate Carleman kernels. Various exact and approximate methods for solving the arising integral equations are applicable.