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We consider the questions of development and substantiation of the reduction of a boundary-value problem for linear and weakly nonlinear integro-dierential equations with parameters and restrictions to an equivalent integral equation without restrictions. The applications of the iterative, projective, and projective-iterative methods to the boundary-value problems for linear integro-dierential equations with parameters and restrictions are studied and justied. Some computational algorithms of the projective-iterative and modied projective-iterative methods for weakly nonlinear integro-dierential equations with parameters and restrictions are proposed.