Summary: ``This paper considers the dependence of eigenvalues of fourth-order differential operator with eigenparameters in the four boundary conditions of both ends of the interval $[a, b]$. It is proved that the eigenvalues depend not only continuously but also smoothly on the parameters of the problem (the coefficient functions, the weight function, the interval endpoints, boundary conditions coefficient matrix), and give the corresponding differential expressions. In particular, the Frechet derivative of the eigenvalue with respect to the eigenparameter-dependent boundary conditions coefficient matrix is given.''