The present paper is a continuation of the paper [9] in which a general iterative method for solving hereditary differential equation is consireded. Using a concept of a bounded integral contractor, sufficient conditions for the existence and uniqueness of a solution of this equation are given. The fact that the Lipschitz condition is equivalent with the existence of the such contractor is proved. It is shown that the iterative procedure, utilised to prove the existence of the solution, is a special algorithm investigated in the paper [9].