New photoluminescence (PL) bands are reported in GaAs doped with Cu and Li as well as with Li only. A study of a PL band at 1.41 eV appearing after both subsequent and simultaneous diffusions of Cu and Li into a range of different GaAs samples under varying doping conditions shows an unequivocal correlation between this band and the presence of both Cu and Li in the samples. Also, an observed decrease of the 1.36-eV Cu PL band as the 1.41-eV Cu-Li band increases suggests a common component of the corresponding two centers, presumably Cu Ga. A model is proposed, assigning the 1.41-eV PL band to recombination involving a 0.11-eV CuGa-Lii acceptor level. It is suggested that a PL peak at 1.34 eV appearing after Li doping of bulk material involves transitions to the doubly ionized LiGa acceptor. Other new PL bands appear after Li diffusion as well. The absence of bound exciton (BE) states associated with these acceptors is also discussed.