  In this work we study the problem of linear stability of gravitational
perturbations in stationary and spherically symmetric wormholes. For this
purpose, we employ the Newman-Penrose formalism which is well-suited for
treating gravitational radiation in General Relativity, as well as the
geometrical aspect of this theory. With this method we obtain a "master
equation" that describes the behavior of gravitational perturbations that are
of odd-parity in the Regge-Wheeler gauge. This equation is later applied to a
specific class of Morris-Thorne wormholes and also to the metric of an
asymptotically flat scalar field wormhole. The analysis of the equations that
these space-times yield reveals that there are no unstable vibrational modes
generated by the type of perturbations here studied.
