  Near-infrared (2.2 $\mu m$) observations of a sample of 48 elliptical
galaxies in the Coma cluster have been carried out and used to study the
near-ir fundamental plane (FP) of ellipticals in this cluster. An rms scatter
of 0.072 dex was found for this relation, similar to that of its optical
counterpart, using the same sample of galaxies. This corresponds to an
uncertainty of 18% in distances to individual galaxies derived from this
relation. The sensitivity of the near-infrared FP to the star formation or
changes in metallicity and stellar population among the ellipticals was
explored and found to be small. Although, a likely source of scatter in this
relation is contributions from the Asymptotic Giant Branch (AGB) population to
their near-infrared light. Allowing for observational uncertainties, we find an
intrinsic scatter of 0.060 dex in the near-ir FP. The cluster galaxies
presented here, provide the zero-point for the peculiar velocity studies, using
the near-infrared FP. Changes in the slopes of the $D-\sigma$ and $L-\sigma$
relations of ellipticals between the optical and near-infrared wavelengths were
investigated and found to be due to variations in metallicity or age (or a
combination of them). However, it was not possible to disentangle the effects
of age and metallicity in these relations. Using evolutionary population
synthesis models, we find that the effects of age and metallicity decouple on
the $(M/L)_K$ vs. Mg$_2$ and $(M/L)_K$ vs. (V$-$K) diagrams.
