  We have studied experimentally the influence of a parallel magnetic field
($B_{//}$) on microwave-induced resistance oscillations (MIRO) and
zero-resistance states (ZRS) previously discovered in a high-mobility 2D
electron system. We have observed a strong suppression of MIRO/ZRS by a modest
$B_{//}\sim 0.5$ T. In Hall bar samples, magnetoplasmon resonance (MPR) has
also been observed concurrently with the MIRO/ZRS. In contrast to the
suppression of MIRO/ZRS, the MPR peak is found to be enhanced by $B_{//}$.
These findings have not been addressed by current models proposed to explain
the microwave-induced effects.
