Fluorescent analogues of nucleobases are very useful as probes to study DNA dynamics, because natural DNA does not fluoresce significantly. In many of these analogues, such as 2-aminopurine (2AP), the fluorescence is quenched when incorporated into DNA through processes that are not well understood. This work uses theoretical studies to examine fluorescence quenching pathways in 2AP-containing dimers. The singlet excited states of pi-stacked dimer systems containing 2AP and a pyrimidine base, thymine or cytosine, have been studied using ab initio computational methods. Computed relaxation pathways along the excited-state surfaces reveal novel mechanisms that can lead to fluorescence quenching in the pi-stacked dimers. The placement of 2AP on the 5' or 3' terminus of the dimers has different effects on the excitation energies and the relaxation pathways on the S-1 excited state. Conical intersections between the ground and first excited states exist when 2AP is placed at the 3' side, whereas the placement of 2AP at the 5' side leads to the switching of a bright state to a dark state. Both of these processes can lead to fluorescence quenching and may contribute to the fluorescence quenching observed in 2AP when incorporated in DNA.