  This study presents a wide-field near-infrared (K-band) survey in two fields;
SA 68 and Lynx 2. The survey covers an area of 0.6 deg.$^2$, complete to
K=16.5. A total of 867 galaxies are detected in this survey of which 175 have
available redshifts. The near-infrared number counts to K=16.5 mag. are
estimated from the complete photometric survey and are found to be in close
agreement with other available studies. The sample is corrected for
incompleteness in redshift space, using selection function in the form of a
Fermi-Dirac distribution. This is then used to estimate the local near-infrared
luminosity function of galaxies. A Schechter fit to the infrared data gives:
M$^\ast_K = -25.1 \pm 0.3$, $\alpha = -1.3\pm 0.2$ and $\phi^\ast =(1.5\pm
0.5)\times 10^{-3}$ Mpc$^{-3}$ (for H$_0=50$ Km/sec/Mpc and q$_0=0.5$). When
reduced to $\alpha=-1$, this agrees with other available estimates of the local
IRLF. We find a steeper slope for the faint-end of the infrared luminosity
function when compared to previous studies. This is interpreted as due to the
presence of a population of faint but evolved (metal rich) galaxies in the
local Universe. However, it is not from the same population as the faint blue
galaxies found in the optical surveys. The characteristic magnitude
($M^\ast_K$) of the local IRLF indicates that the bright red galaxies ($M_K\sim
-27$ mag.) have a space density of $\le 5\times 10^{-5}$ Mpc$^{-3}$ and hence,
are not likely to be local objects.
