EOM-CCSD and CC2-LR methods were used to study the potential energy surfaces of the three lowest excited states (two pi pi* and an n pi*) of adenine. The equilibrium structure could only be obtained for the S-1 state, which has n-pi* character. It was shown that the topology of the coupled cluster surface is such that no minimum for the S-2 and S-3 states exists in the Franck-Condon region due to conical intersections between these low-lying states. To understand this topology, relevant cuts of the potential energy surfaces have also been calculated, and conical intersections have been located. Even a three-fold intersection between these three states was found. The crossings of these surfaces can be reached from the bright state barrierlessly without major change in the geometry. Therefore, these might play an important role in the ultrafast deactivation of adenine.