  This article deals with the multidimensional Borg-Levinson theorem for
perturbed bi-harmonic operator. More precisely, in a bounded smooth domain of
$\R^n$, with $n \geq 2$, we prove the stability of the first and zero order
coefficients of the bi-harmonic operator from some asymptotic behavior of the
boundary spectral data of the corresponding bi-harmonic operator i.e., the
Dirichlet eigenvalues and the Neumann trace on the boundary of the associated
eigenfunctions.
