  We present near-infrared (NIR) spectroscopic observations of the blue compact
dwarf (BCD) galaxy Mrk 59, obtained with the TripleSpec spectrograph mounted on
the 3.5m APO telescope. The NIR spectrum of Mrk 59, which covers the 0.90 -
2.40 micron wavelength range, shows atomic hydrogen, molecular hydrogen,
helium, sulfur and iron emission lines. The NIR data have been supplemented by
a SDSS optical spectrum. We found extinction in the BCD to be low [A(V)=0.24
mag] and to be the same in both the optical and NIR ranges. The NIR light does
not reveal hidden star formation. The H2 emission comes from dense clumps and
the H2 vibrational emission line intensities can be accounted for by photon
excitation. No shock excitation is needed. A CLOUDY photoinization model of Mrk
59 reproduces well the observed optical and NIR emission line fluxes. There is
no need to invoke sources of ionization other than stellar radiation.The [FeII]
1.257 and 1.643 micron emission lines, often used as supernova shock indicators
in low-excitation high-metallicity starburst galaxies, cannot play such a role
in high-excitation low-metallicity HII regions such as Mrk 59.
