Stability of a cosmological model with dynamical cancellation of vacuum energy

The stability of cosmological solutions in the recently suggested specific mechanism of dynamical compensation of vacuum energy is studied. It is found that the solutions in the original version lead to cosmological singularity which could be reached in final (and short) time. A modification of the interaction of the compensating field with gravity is suggested which allows to escape such singularity. It is shown that generic cosmological solution in this model tends to the Friedmann expansion regime even starting from initially large vacuum energy.