  Double porosity models for the liquid filtration in an absolutely rigid body
is derived from homogenization theory. The governing equations of the fluid
dynamics on the microscopic level consist of the Stokes system for a slightly
compressible viscous fluid, occupying a crack -- pore space. In turn, this
domain is a union of two independent systems of cracks (fissures) and pores. We
suppose that the dimensionless size $\delta$ of pores depends on the
dimensionless size $\varepsilon$ of cracks: $\delta=\varepsilon^{r}$ with
$r>1$. The rigorous justification is fulfilled for homogenization procedure as
the dimensionless size of the cracks tends to zero, while the solid body is
geometrically periodic. As a result, for the long-time process we derive the
usual Darcy equations of filtration for the liquid in cracks, while the liquid
in pores is blocked and unmoved. For the short-time processes the homogenized
system consists of acoustic equations, describing a two-velocity continuum with
three independent parameters: the liquid velocity in pores, the liquid velocity
in cracks and the common pressure. The proofs are based on the method of
reiterated homogenization, suggested by G. Allaire and M. Briane.
