  This paper studies asymptotic behavior of solutions of a free boundary
problem modeling the growth of tumors with two species of cells: proliferating
cells and quiecent cells. In previous literatures it has been proved that this
problem has a unique stationary solution which is asymptotically stable in the
limit case $\varepsilon=0$. In this paper we consider the more realistic case
$0<\varepsilon<<1$. In this case, after suitable reduction the model takes the
form of a coupled system of a parabolic equation and a hyperbolic system, so
that it is more difficult than the limit case $\varepsilon=0$. By using some
unknown variable transform as well as the similarity transform technique
developed in our previous work, we prove that the stationary solution is also
asymptotically stable in the case $0<\varepsilon<<1$.
