The authors continue the investigation [cf. the first author and L. Z. Vitova, Litov. Mat. Sb. 15, No.2, 41-47 (1975; Zbl 0321.45006)] of the integral operators \[ Au(x,y)=\int^{1}_{0}K(x,s)u(s,y)ds+\int^{1}_{0}N(y,t)u(x,t)dt \] with K(x,y) and N(x,y) being the kernels of compact selfadjoint operators in the space \(L_ 2([0,1])\).