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Let T be a time scale not bounded below and above such that to e T. In this paper, we provide new sufficient conditions and use the Banach fixed point theorem to establish the stability results about the zero solution for the following Levin-Nohel intego-dynamic equation with variable delay ... where xΔ is Δ-derivative on T. An asymptotic stability theorem with a necessary and sufficient condition is proved. In addition, the case of the equation with several delays is studied. The results obtained here extend the work of Bessioud, Ardjouni, Djoudi [10] [ABSTRACT FROM AUTHOR]