Symmetric centrosymmetric and symmetric skew-centrosymmetric matrices are two classes of important matrices in many real world applications. In addition, there have been many papers studying the numerical methods for matrix equations and eigenproblems of these two classes of matrices. It is well-known that backward errors are very important for assessing the stability and quality of numerical algorithms. In this talk, we will present explicit formulae of backward errors in the eigenproblems of symmetric centrosymmetric matrices and symmetric skew-centrosymmetric matrices, respectively.