Experimental measurements of various nonlinear effects in a driven vibrating wire have been reported [Hanson et al., J. Acoust. Soc. Am. 96, 1549--1556 (1994)]. Notable effects observed at driving frequencies near a natural resonance included the generation of motion perpendicular to the plane of the driving force, sudden jumps in amplitude and phase, whirling motion, and hysteresis. Reported here are results of amplitude and phase measurements of generated second, third, and fourth harmonics of the driving frequency, both in the plane of the driving force (vertical) and perpendicular to it. These higher harmonics, which are not significant at frequencies far off resonance, become very significant near a resonance. In some regions the amplitude of the horizontal motion exceeds that of the vertical motion of the same harmonic. If a twist (10--130 deg) is introduced before the wire is clamped, significant amplitude changes of the higher harmonics are observed. Under some conditions, when the wire is driven at frequencies near its third natural resonance, a very pronounced subharmonic splitting of order three is observed. Related effects are also observed for a wire vibrating freely after a pluck. Qualitative aspects will be illustrated on video tape.