  The decay rates of the density-density correlation function are computed for
a chaotic billiard with some amount of disorder inside. In the case of the
clean system the rates are zeros of Ruelle's Zeta function and in the limit of
strong disorder they are roots of Selberg's Zeta function. We constructed the
interpolation formula between two limiting Zeta functions by analogy with the
case of the integrable billiards. The almost clean limit is discussed in some
detail. PACS numbers: 05.20.Dd, 05.45.+b, 51.10.+y
