Approximate methods of solving Cauchy problem for functional-differential equations

We offer a method of approximate solution of abstract functional-differential equation in arbitrary Banah functional spaces. The met hod is based on substitution an operator of volterra on a close operator, which possesses a property of T - kvasivolterrovosty. If approximate operator will be chosen properly then from this method we can get new and known methods of solution of concrete functional-differential equations.