A model for the ab initio treatment of the Renner-Teller effect in tetra-atomic molecules is elaborated. It is based on the approach developed by Petelin and Kiselev [Int. J. Quantum Chem, 6, 701 (1972)]. Particular attention is paid to Pi electronic states, Perturbative formulas are derived for several coupling cases. The model is checked by means of nb initio calculations at various levels of sophistication. Results of computations of various quantities related to the model are presented for the X(2) Pi(u) stares of B2H2+ and C2H2+. The reliability of the basis assumptions is demonstrated by comparing the results obtained in the framework of the model consider-ed with those of independent ab initio calculations.