We present orbital-phase resolved I and K-band spectroscopy of Cygnus
X-3. All spectra show emission lines characteristic of Wolf-Rayet star
s of the WN subclass. On time scales longer than about one day, the li
ne strengths show large changes, both in flux and in equivalent width.
In addition, the line ratios change, corresponding to a variation in
spectral subtype of WN6/7 to WN4/5. We confirm the finding that at tim
es when the emission lines are weak, they shift in wavelength as a fun
ction of orbital phase, with maximum blueshift coinciding with infrare
d and X-ray minimum, and maximum redshift half an orbit later. Further
more, we confirm the prediction - made on the basis of previous observ
ations - that at times when the emission lines are strong, no clear wa
velength shifts are observed. We describe a simplified, but detailed m
odel for the system, in which the companion of the X-ray source is a W
olf-Rayet star whose wind is at times ionised by the X-ray source, exc
ept for the part in the star's shadow. With this model, the observed s
pectral variations can be reproduced with only a small number of free
parameters. We discuss and verify the ramifications of this model, and
find that, in general, the observed properties can be understood. We
conclude that Cyg X-3 is a Wolf-Rayet/X-ray binary.