We present a development of the dipole moment and polarizability operators of X$_2$Y$_4$ molecules, using a tensorial formalism} {\bf 217}, 239-248, (2003)}$^,$}, accepted, (2005).} analogous to the one developed for tetrahedral and octahedral molecules} {\bf 228}, 620-634, (2004).}. These operators are involved in the calculation of the intensities of rovibrational transitions as well as in the calculation of the Stark effect. Expressions for the matrix elements are derived. A model for the study of the Stark effect in isolated bands of such molecules is proposed and has been used to predict the Stark spectra of the $ν_{12}$ band of ethylene. Values of the polarizability coefficients have been calculated using {\em ab initio} methods. ; {W. Raballand, M. Rotger, V. Boudon and M. Loete, {\em J. Mol. Spectrosc.{Ch. Wenger, W. Raballand, M. Rotger and V. Boudon, {\em J. Quant. Spectrosc. Radiat. Transfer{V. Boudon, J.-P. Champion, T. Gabard, M. Loete, F. Michelot, G. Pierre, M. Rotger, Ch. Wenger and M. Rey, {\em J. Mol. Spectrosc. ; Author Institution: Laboratoire de Physique de l'Uni\-versite de Bourgogne,; UMR CNRS 5027, 9, av. Alain Savary, B.P. 47870, F-21078 Dijon Cedex, France; Max-Planck-Institut fur Kohlenforschung, Kaiser-Wilhelm-Platz 1, D-45470 Mulheim an der Ruhr, Germany