  We study pulsating strings both on a single stack of NS5-branes and two
orthogonal stacks of NS5-branes (the so called I-brane) by using the Polyakov
form of the fundamental string action. For the I-brane background, by using a
symmetry that decouples the two spheres from the flat geometry, we study
pulsating solutions of the string when it pulsates on both the spheres
independently and simultaneously. We finally derive the energy of pulsating
strings as a function of adiabatic invariant oscillation number in these cases
and studied some limiting cases in detail.
