  Let $G$ be a finite group and $\Z G$ its integral group ring. We show that if
$\alpha$ is a non-trivial bicyclic unit of $\Z G$, then there are bicyclic
units $\beta$ and $\gamma$ of different types, such that $\GEN{\alpha,\beta}$
and $\GEN{\alpha,\gamma}$ are non-abelian free groups. In case that $G$ is
non-abelian of order coprime with 6, then we prove the existence of a bicyclic
unit $u$ and a Bass cyclic unit $v$ in $\Z G$, such that for every positive
integer $m$ big enough, $\GEN{u^m,v}$ is a free non-abelian group.
