The dynamics of vertically compensated two-layer vortices (hetons) with fin
ite cores are examined within the context of the quasi-geostrophic approxim
ation on the f-plane. The two-layer version of the contour dynamics method
is used, and complemented by the so-called contour surgery technique. Speci
al attention is paid to two-heton interactions when the initial locations o
f the vortex patches are symmetrical. A classification of the different reg
imes observed is made according to external parameters, namely geometrical
parameters and stratification. In this parameter space, novel quasi-station
ary states resulting from collisions between two hetons may be observed: (i
) formation of a configuration consisting of two-layer vortices moving in o
pposite directions and, as a special case, a configuration analogous to the
'klapstoss' billiard shot, (ii) absorption of one heton by the other and s
ubsequent movement of a new dipole, (iii) formation of two-layer dipoles, l
arger than the original hetons, associated with rotating peripheral satelli
te eddies in their wakes. Some of these results may have implications for t
he analysis of mesoscale vortices in the ocean.