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We study oscillating string solutions in the Klebanov-Witten and itsnon-Abelian T-dual background dualised along an SU(2) isometry. We find thestring energy as the function of oscillation number and angular momentum. Weshow that for a particular set of T-dual co-ordinates both the background haveequal string states. We also study the string states where the strings areexpanding and contracting in the T-dual co-ordinate direction. We expect thepresence of the superconformal field theory dual operators whose anomalousdimensions depend on T-dual co-ordinate.

Oscillating Strings and Non-Abelian T-dual Klebanov-Witten Background