In the present work, an alternative family of analytical potential energy curves (PECs) has been developed for diatomic systems. These kinds of functions, that are based on q-exponential, are used here to generalize the usual Bond Order (BO) and Rydberg analytical PECs of diatomic molecular systems. The diatomic systems H-2(+) and Li-2 have been examined by means of this alternative approach. In particular, the computed vibrational spectra and spectroscopic constants were found to be in good agreement with the available experimental data. (c) 2006 Elsevier B.V.All rights reserved.