  We conduct spectral observations of 138 superthin galaxies (STGs) with high
radial-to-vertical stellar disk scales ratio with the Dual Imaging Spectrograph
(DIS) on the 3.5m telescope at the Apache Point Observatory (APO) to obtain the
ionized gas rotation curves with R ~ 5000 resolution. We also performed near
infrared (NIR) H and Ks photometry for 18 galaxies with the NICFPS camera on
the 3.5m telescope. The spectra, the NIR photometry and published optical and
NIR photometry are used for modeling that utilizes the thickness of the stellar
disk and rotation curves simultaneously. The projection and dust extinction
effects are taken into account. We evaluate eight models that differ by their
free parameters and constraints. As a result, we estimated masses and scale
lengths of the galactic dark halos. We find systematic differences between the
properties of our red and blue STGs. The blue STGs have a large fraction of
dynamically under-evolved galaxies whose vertical velocity dispersion is low in
both gas and stellar disks. The dark halo-to-disk scale ratio is shorter in the
red STGs than in the blue ones, but in a majority of all STGs this ratio is
under 2. The optical color $(r-i)$ of the superthin galaxies correlates with
their rotation curve maximum, vertical velocity dispersion in stellar disks,
and mass of the dark halo. We conclude that there is a threshold central
surface density of 50 $M_{\odot}$\,pc$^{-2}$ below which we do not observe very
thin, rotationally supported galactic disks.
