This paper deals with the nonconforming spectral approximation of variationally posed eigenvalue problems. It is an extension to more general situations of known previous results about nonconforming methods. As an application of the present theory, convergence and optimal order error estimates are proved for the lowest order Crouzeix-Raviart approximation of the eigenpairs of two representative second-order elliptical operators.Facultad de Ciencias Exactas