Abstract. The Liouville tori, having an integrable metric of the form (U1(q1)− U2(q2))(dq 2 1 + dq 2 ), allow the separation of variables in the study of the Laplacian spectrum. The asymptotic analysis of the resulting Sturm-Liouville problems allows to reduce the count of the eigenvalues of the spectrum to the count of the lattice points inside a plane domain. The present paper is concerned wi...