We present data from high-dispersion echelle spectra and simultaneous $uvby$ photometry for $gamma$~Doradus. These data were obtained from several sites during 1994 November as part of the MUSICOS-94 campaign. The star has two closely-spaced periods of about 0.75 d and is the brightest member of a new class of variable early F-type stars. A previously suspected third period, very close to the other two, is confirmed. Previous observations indicated that sudden changes could be expected in the spectrum, but none were found during the campaign. The radial velocities rule out the possibility of a close companion. The phasing between the radial velocity and light curve of the strongest periodic component rules out the starspot model. The only viable mechanism for understanding the variability is nonradial pulsation. We used the method of moments to identify the modes of pulsation of the three periodic components. These appear to be sectorial retrograde modes with spherical harmonic degrees, ($ell, m$), as follows: $f_1$ = (3,3), $f_2$ = (1,1) and $f_4$ = (1,1). The angle of inclination of the star is found to be $i approx 70^circ$.
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