  The cosmological constant problem is studied in a two component cosmological
model. The universe contains a cosmological constant of an arbitrary size and
sign and an additional component with an inhomogeneous equation of state. It is
shown that, in a proper parameter regime, the expansion of the universe with a
large absolute value of the cosmological constant may asymptotically tend to de
Sitter space corresponding to a small effective positive cosmological constant.
It is argued that such a behavior can be regarded as a solution of the
cosmological constant problem in this model. The mechanism behind the
relaxation of the cosmological constant is discussed. A connection with
modified gravity theories is discussed and an example of a possible realization
of the cosmological constant relaxation in f(R) modified gravity is described.
