Summary: Many mathematical models of biological processes can be represented as free boundary problems for systems of PDEs. In the radially symmetric case, the free boundary is a function of \(r=R(t)\), and one can generally prove the existence of global in-time solutions. However, the asymptotic behavior of the solution and, in particular, of \(R(t)\), has not been explored except in very special cases. In the present paper we consider two such models which arise in cancer treatment by combination therapy with two drugs. We study the asymptotic behavior of the solution and its dependence on the dose levels of the two drugs.