The gas-phase photoelectron spectrum of water in the 12-20 eV energy range is simulated. The potential energy surfaces (PESs) of the three cationic states involved show several degeneracies. The ground state ((XB1)-B-2) and the first excited state (A(2)A(1)) are degenerate components of a (2)Pi(u) state in linear geometry leading to Renner-Teller coupling while the PESs of the A state and the second excited state ((BB2)-B-2) exhibit a conical intersection. Thus, an adiabatic approach that relies on sufficiently separated surfaces deems inappropriate. However, an orthogonal transformation of the electronic states removes the diverging matrix elements in the kinetic energy. These diabatic states permit a correct treatment of the nuclear dynamics near a conical intersection as well as in the Renner-Teller zone. The quantum mechanical equations of motion of the nuclei are solved using the multiconfiguration time-dependent Hartree (MCTDH) method. Quantum chemical calculations for the cationic states had been performed before, using a multireference configuration interaction method.