  We present a cosmological model containing a cosmological constant $\Lambda$
and a component with an inhomogeneous equation of state. We study the form of
the inhomogeneous equation of state for which the model exhibits the relaxation
of the cosmological constant, i.e. it asymptotically tends to the de Sitter
regime characterized by a small positive effective cosmological constant. The
effect of the relaxation of the cosmological constant is observed both for
negative and positive values of $\Lambda$ and for a range of model parameters.
A special emphasis is put on the study of the details of the CC relaxation
mechanism and the robustness of the mechanism to the variation of model
parameters. It is found that within the studied model the effective
cosmological constant at large scale factor values is small because the
absolute value of the real cosmological constant is large.

General Relativity and Quantum Cosmology