  Let $(\FormR)$ be a form ring such that $A$ is quasi-finite $R$-algebra
(i.e., a direct limit of module finite algebras) with identity. We consider the
hyperbolic Bak's unitary groups $\GU(2n,\FormR)$, $n\ge 3$. For a form ideal
$(I,\Gamma)$ of the form ring $(\FormR)$ we denote by $\EU(2n,I,\Gamma)$ and
$\GU(2n,I,\Gamma)$ the relative elementary group and the principal congruence
subgroup of level $(I,\Gamma)$, respectively. Now, let $(I_i,\Gamma_i) $,
$i=0,...,m$, be form ideals of the form ring $(A,\Lambda)$. The main result of
the present paper is the following multiple commutator formula
[\big[\EU(2n,I_0,\Gamma_0),&\GU(2n,I_1,\Gamma_1),\GU(2n, I_2,\Gamma_2),...,
\GU(2n,I_m,\Gamma_m)\big]=
&\big[\EU(2n,I_0,\Gamma_0),\EU(2n,I_1,\Gamma_1),\EU(2n,I_2,\Gamma_2),...,
\EU(2n, I_m, \Gamma_m)\big],] which is a broad generalization of the standard
commutator formulas. This result contains all previous results on commutator
formulas for classical like-groups over commutative and finite-dimensional
rings.
