Conical intersections (CIs) play an important role in nonadiabatic molecular processes. We pointed out, that the Renner effect in polyatomic molecules is accompanied by symmetry-allowed CIs. Ab initio calculations and a perturbational approach have confirmed that two aligned CIs are created in the slightly bent C2H2+ molecule. In contrast, different results were obtained for the H2CN molecule. To understand this new phenomenon, additional more detailed investigations have been performed for selected Renner-Teller systems. (C) 2011 Elsevier B. V. All rights reserved.