Abstract. Let N be an integral operator of the formacting in Lp(R c ) with a measurable kernel n satisfying the estimatewhere β ∈ L 1 . It is proved that if the function t → n(t, ·) is continuous in the norm of L 1 and the operator 1 + N has an inverse, then (1 + N ) −1 = 1 + M , where M is an integral operator possessing the same properties.