We investigate numerically the possibility that dissipationless cosmol
ogical collapses can lead to the formation of counterrotating galaxies
. We consider systems formed from initially small density excesses emb
edded in the environment of other density perturbations in an otherwis
e homogeneous and isotropic expanding early Universe. We find that a c
entral bar-like density excess, that can make bound a mass of the orde
r of galactic mass can work as a seed able to initiate counterrotating
galaxies. Such objects are formed rather naturally as a result of the
partial mixing between the material in which positive angular momentu
m dominates with the material in which negative angular momentum domin
ates. The initial axial ratio of the bar-like perturbation is a contro
l parameter in this process. Counterrotation is favored for an axial r
atio approximate to 0.5. The rotational velocity profile in the relaxe
d state of these configurations matches to a great extent the curves g
iven from observations, for some elliptical galaxies, presenting kinem
atically decoupled cores. Performing parallel simulations of the same
system by N-body and by conservative technique codes we show that the
rotational velocity curve, established after the relaxation, maintains
its basic features even for a Hubble time. Therefore counterrotating
galaxies observed today could have been formed directly from cosmologi
cal initial conditions.