  A sample of 27 disturbed galaxies that show signs of interaction but have a
single nucleus were selected from the Arp and the Arp-Madore catalogues. For
these, the K_s band images from the Two Micron All Sky Survey (2MASS) are
analysed to obtain their radial luminosity profiles and other structural
parameters. We find that in spite of their similar optical appearance, the
sample galaxies vary in their dynamical properties, and fall into two distinct
classes. The first class consists of galaxies which can be described by a
single r^{1/4} law and the second class consists of galaxies that show an outer
exponential disk. A few galaxies that have disturbed profiles cannot be fit
into either of the above classes. However, all the galaxies are similar in all
other parameters such as the far-infrared colours, the molecular hydrogen
content and the central velocity dispersion. Thus, the dynamical parameters of
these sets seem to be determined by the ratio of the initial masses of the
colliding galaxies. We propose that the galaxies in the first class result from
a merger of spiral galaxies of equal masses whereas the second class of
galaxies results from a merger of unequal mass galaxies. The few objects that
do not fall into either category show a disturbed luminosity profile and a
wandering centre, which is indicative of these being unrelaxed mergers. Of the
27 galaxies in our sample, 9 show elliptical-like profiles and 13 show an outer
exponential. Interestingly, Arp 224, the second oldest merger remnant of the
Toomre sequence shows an exponential disk in the outer parts.
