  Motivated by the possibility of $H_0t_0 > 1$ where $H_0$ and $t_0$ are the
Hubble parameter and the age of the universe, respectively, we investigate the
cosmology including x-matter. x-matter is expressed by the equation of state
$p_x=w_0\rho_{x0} + c_s^2(\rho_x-\rho_{x0})$, where $p_x$, $\rho_x$ and
$\rho_{x0}$ are the pressure, the density of x-matter and the density at
present, respectively. $w_0$ and $c_s^2$ are functions of $\rho_x$ in general.
x-matter has the most general form of the equation of state which is
characterized by 1)violation of strong energy condition at present for $w_0 <
-1/3$ ; 2) locally stable (i.e. $c_s^2\geq 0$); 3)causality is guaranteed
($c_s\leq 1$). Considering the case that $w_0$ and $c_s^2$ are constants, we
find that there is a large parameter space of $(w_0,c_s^2,\Omega_{x0})$ in
which the model universe is consistent with the age of the universe and the
observations of distant Type I supernovae.
