  The Heider theory of cognitive dissonance in social groups, formulated
recently in terms of differential equations, is generalized here for the case
of asymmetric interpersonal ties. The space of initial states is penetrated by
starting the time evolution several times with random initial conditions.
Numerical results show the fat-tailed distribution of the time when the
dissonance is removed. For small groups (N=3) we found some characteristic
patterns of the long-living states. There, mutual relations of one of the pairs
differ in sign.
