In this article we constructed an asymptotic expansion of the solution undivided boundary value problem for singularly perturbed integro-differential equations with an initial jump phenomenon m – th order. We obtain the theorem about estimation of the remainder term’s asymptotic with any degree of accuracy in the smallparameter.

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The paper considers the extension of Tikhonov Theorem for singularly perturbed differential equation with piecewise constant argument of generalized type. An approximate solution of the problem has been obtained. A new phenomenon of humping has been observed in the boundary layer area. An illustrative example with simulations is provided.