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Abstract In this paper, based on simple analytic techniques, we explore the integrability conditions for classical stringy configurations defined over η as well as λ-deformed backgrounds. We perform our analysis considering classical string motions within various subsectors of the full target space geometry. It turns out that classical string configurations defined over η-deformed backgrounds are non-integrable whereas on the other hand, the corresponding configurations are integrable over the λ-deformed background. Our analysis therefore imposes a strong constraint on the operator spectrum associated with the corresponding dual gauge theories at strong coupling.