We present a framework for reducing all possible cohomogeneity-one strings,<br />
i.e., strings with geometrical symmetry, in a given spacetime to mechanical<br />
systems, and for analyzing integrability of the systems. As applications, it is<br />
clarified whether the systems of cohomogeneity-one strings in $AdS_5$, $AdS_5<br />
\times S^5$, and $AdS_5 \times T^{p,q}$ are integrable or not. This method may<br />
reveal a different type of hidden symmetry of spacetimes.