We present the basic system of equations for a theory of superconductivity forsystems with chaotically distributed paramagnetic impurities of substitution inwhich the Migdal theorem is violated (it cannot be supposed ω0 ≪ EF ).We take into account electron–phonon and impurity diagrams aswell as supplementary ones corresponding to the intersection ofelectron–phonon and electron–impurity lines. Decrease of the quantityTC withincrease of impurity concentration is shown to weaken in comparison with the case ofthe usual superconductors. The degree of this decrease is determined by quantitiesm andqc.The coefficient of the isotope effect α, energy gap and orderparameter at T = 0are also calculated. The behaviour of these quantities as a function ofimpurity concentration depends on the Migdal parameter m = ω0 /EF and transferredmomentum qc.