In this Letter we present two conical intersection lines (CLs) between adiabatic potential energy surfaces (PESs) of oxonium correlated to the asymptotic systems H + H2O+((X) over tilde), H+ + H2O+(X) over tilde and H + H2O+((A) over tilde). Such PESs features are related to the dynamics of the charge transfer process H+ + H2O --> H + H2O+ studied by Toennies and coworkers. A new three steps method is also presented whereby to determine the CLs. The generalized Heitler-London approximation is used first to obtain the analytical expression of a qualitative CL in whose neighborhood the accurate CL is finally ab initio computed after an intermediate searching step. Using this strategy the 3D configurational subspace where to search for crossing points is drastically reduced allowing for a faster determination of the CLs. (C) 2003 Elsevier Science B.V. All rights reserved.