  We study the influence of an external magnetic field on the collective
electronic excitations in metallic nanoparticles. While the usual surface
plasmon corresponding to the collective oscillation of the electrons with
respect to the ionic background persists in the direction parallel to the
magnetic field, the components in the perpendicular plane are affected by the
field and give rise to two collective modes with field-dependent frequencies,
the surface magnetoplasmons. We analyze the decay of these collective
excitations by their coupling to particle-hole excitations and determine how
their lifetimes are modified by the magnetic field. In particular, we show that
the lifetime of the usual surface plasmon is not modified by the magnetic
field, while the lifetime of the two surface magnetoplasmons present a weak
magnetic-field dependence. Optical spectroscopy experiments are suggested in
which signatures of the surface magnetoplasmons may be observed.
