The neutral donor bound exciton recombination processes in freestanding GaN have been studied. The photoluminescence spectrum shows emission lines related to silicon and oxygen donors. Time-resolved luminescence allows us to correlate the principal donor bound exciton lines with their two-electron satellites. The magnetic field splitting of the two-electron lines is well described by the theory of the hydrogen atom in a magnetic field. For the oxygen donor a 1.5 meV chemical shift and a 30.8 meV effective Rydberg have been evaluated. Two-electron satellites involving excitations to the 2p and 2s donor states are separated by an energy of 1.0 and 1.3 meV for O and Si impurity, respectively. The temperature dependence of the two-electron emission clearly shows that this separation arises from a splitting of the ground state of the neutral donor bound exciton complex. The nature of this splitting is discussed and it is suggested that it is due to rotational states of donor bound excitons.