  We present observations and models of the behaviour of the HI and HeI lines
between 1.6 and 2.2um in a small sample of compact HII regions. As in our
previous papers on planetary nebulae, we find that the `pure' 1.7007um
4^3D-3^3P and 2.16475um 7^(3,1)G-4^(3,1)F HeI recombination lines behave
approximately as expected as the effective temperature of the central exciting
star(s) increases. However, the 2.058um 2^1P-2^1S HeI line does not behave as
the model predicts, or as seen in planetary nebulae. Both models and planetary
nebulae showed a decrease in the HeI 2^1P-2^1S/HI Br gamma ratio above an
effective temperature of 40000K. The compact HII regions do not show any such
decrease. The problem with this line ratio is probably due to the fact that the
photoionisation model does not account correctly for the high densities seen in
these HII regions, and that we are therefore seeing more collisional excitation
of the 2^1P level than the model predicts. It may also reflect some deeper
problem in the assumed model stellar atmospheres. In any event, although the
normal HeI recombination lines can be used to place constraints on the
temperature of the hottest star present, the HeI 2^1P-2^1S/HI Br gamma ratio
should not be used for this purpose in either Galactic HII regions or in
starburst galaxies, and conclusions from previous work using this ratio should
be regarded with extreme caution. We also show that the combination of the near
infrared `pure' recombination line ratios with mid-infrared forbidden line data
provides a good discriminant of the form of the far ultraviolet spectral energy
distribution of the exciting star(s). From this we conclude that CoStar models
are a poor match to the available data for our sources, though the more recent
WM-basic models are a better fit.
