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We investigated gamma- and neutron-scintillation properties of A2LiLnX6:Ce3+ (A=Cs, Rb, K, Na, Li; Ln=La, Y, Lu, Sc; X=Br, I) with the aim to develop new scintillators with high neutron detection efficiencies. Among the investigated thermal neutron scintillators, Rb2LiYBr6:Ce3+ shows an excellent neutron peak resolution of 3.6%. This is the best neutron peak resolution ever reported. Together with the large alpha/beta ratio of 0.74, Rb2LiYBr6:Ce3+ offers the possibility of excellent neutron/gamma discrimination. The highest thermal neutron scintillation light yield of 83,000 photons/neutron is also reported for Rb2LiYBr6:Ce3+.