  We study finitely-generated nondiscrete free subgroups in Lie groups. We
address the following question first raised by \'Etienne Ghys: is it always
possible to make arbitrarily small perturbation of the generators of the free
subgroup in such a way that the new group formed by the perturbed generators be
not free? In other words, is it possible to approximate generators of a free
subgroup by elements satisfying a nontrivial relation? We prove that the answer
to Ghys' question is positive and generalize this result to certain non-free
subgroups. We also consider the question on the best approximation rate in
terms of the minimal length of relation in the approximating group. We give an
upper bound on the optimal approximation rate as $e^{-cl^{\kappa}}$, where
$c>0$ is a constant, $l$ the minimal length of relation and $0.19<\kappa<0.2$.
