We discuss the spectral properties of a linear operator generated by a differential expression and the boundary conditions. We also consider operators, which are the correct extensions of a minimal operator. It is assumed that the boundary conditions are regular in the sense that the inverse operator exists and ensure certain smoothness of the domain of the original operator. Under this assumption, the spectrum of an operator can consist only the eigenvalues of finite multiplicity. Under sufficiently general assumptions, it is proved that the spectrum of the operator is either empty or infinite. that is the operator cannot have a finite number of eigenvalues.