  We study semi-classically the dynamics of string solitons in the
Maldacena-Nunez background, dual in the infra-red to N=1, d=4 SYM. For closed
string configurations rotating in the S^2 x R space wrapped by the stack of N
D-branes we find a behavior that indicates the decoupling of the stringy
Kaluza-Klein modes with sufficiently large SO(3) quantum numbers. We show that
the spectrum of a pulsating string configuration in S^2 coincides with that of
a N=2 super Sine-Gordon model. Closed string configurations spinning in the
transversal S^3 give a relation of the energy and the conserved angular
momentum identical to that obtained for configurations spinning in the S^5 of
the AdS_5 x S^5, dual to N =4 SYM. In order to obtain non-trivial relations
between the energy and the spin, we also consider conical-like configurations
stretching along a radial variable in the unwrapped directions of the system of
D-branes and simultaneously along the transversal direction. We find that in
this precise case, these configurations are unstable --contrary to other
backgrounds, where we show that they are stable. We point out that in the
Poincare-like coordinates used for the Maldacena-Nunez background it seems that
it is not possible to reproduce the well-known field theory relation between
the energy and the angular momentum. We reach a similar conclusion for the
Klebanov-Strassler background, by showing that the conical-like configurations
are also unstable.
