  We present a calculation of the properties of vibrational states in deformed,
axially--symmetric even--even nuclei, within the framework of a fully
self--consistent Quasparticle Random Phase Approximation (QRPA). The same
Skyrme energy density and density-dependent pairing functionals are used to
calculate the mean field and the residual interaction in the particle-hole and
particle-particle channels. We have tested our software in the case of
spherical nuclei against fully self consistent calculations published in the
literature, finding excellent agreement. We investigate the consequences of
neglecting the spin-orbit and Coulomb residual interactions in QRPA.
Furthermore we discuss the improvement obtained in the QRPA result associated
with the removal of spurious modes. Isoscalar and isovector responses in the
deformed ${}^{24-26}$Mg, $^{34}$Mg isotopes are presented and compared to
experimental findings.
