  A general class of rotating closed string solutions in AdS_5 x S^5 is shown
to be described by a Neumann-Rosochatius one-dimensional integrable system. The
latter represents an oscillator on a sphere or a hyperboloid with an additional
``centrifugal'' potential. We expect that the reduction of the AdS_5 x S^5
sigma model to the Neumann-Rosochatius system should have further
generalizations and should be useful for uncovering new relations between
integrable structures on the two sides of the AdS/CFT duality. We find, in
particular, new circular rotating string solutions with two AdS_5 and three S^5
spins. As in other recently discussed examples, the leading large-spin
correction to the classical energy turns out to be proportional to the square
of the string tension or the 't Hooft coupling \lambda, suggesting that it can
be matched onto the one-loop anomalous dimensions of the corresponding ``long''
operators on the SYM side of the AdS/CFT duality.
