  We use the integral form of the Boltzmann equation which allows us to take
into account the memory effects using the initial condition that selects the
solutions going to the local equilibrium Maxwell distribution in the $t \to
-\infty$ limit. Implementing the relaxation-time approximation for the
collision integral (BGK-equation) we present the derivation of the hyperbolic
Navier-Stokes and the hyperbolic heat conduction equations in the first order
approximation. It is shown that the relaxation time in the obtained hyperbolic
equations is the Maxwellian relaxation time. As special case we obtain the
telegraph equation for the heat propagation in static medium and estimate the
relaxation time for the heat conduction in some materials.
