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Alkali dimers are widely used in modern fundamental studies devoted to the “weak sides” of the Standard Model, like dark matter, dark energy, matter-antimatter asymmetry [D. DeMille, J.M. Doyle, A.O. Sushkov, Science 357, 990 (2017)]. In order to perform such experiments the precise data on their energy structure and radiative properties are needed [E.A. Pazyuk, A.V. Zaitsevskii, A.V. Stolyarov, M. Tamanis, R. Ferber, Russ. Chem. Rev. 84, 1001 (2015)]. In this study the accurate ab initio relativistic functions of the static and transition dipole moments for the low-lying electronic LiM (M=Rb, Cs) states are presented.