[en] We study the weak decays of anti B_(_s_) and B_c into D-wave heavy-light mesons, including J"P = 2"- (D_(_s_)_2, D_(_s_)_2"', B_(_s_)_2, B_(_s_)_2"') and 3"- (D"*_(_s_)_3, B"*_(_s_)_3) states. The weak decay hadronic matrix elements are obtained based on the instantaneous Bethe-Salpeter method. The branching ratios for the anti B decays are B[ anti B → D_2e anti ν_e] = 1.1"-"0"."3_+_0_._3 x 10"-"3, B[ anti B → D_2"'e anti ν_e] = 4.1"-"0"."8_+_0_._9 x 10"-"4, and B[ anti B → D_3"*e anti ν_e] = 1.0"-"0"."2_+_0_._2 x 10"-"3, respectively. For the semi-electronic decays of anti B_s to D_s_2, D_s_2"', and D"*_s_3, the corresponding branching ratios are 1.7"-"0"."5_+_0_._5 x 10"-"3, 5.2"-"1"."5_+_1_._6 x 10"-"4, and 1.5"-"0"."4_+_0_._4 x 10"-"3, respectively. The branching ratios of the semi-electronic decays of B_c to D-wave D mesons are in the order of 10"-"5. We also obtained the forward-backward asymmetry, angular spectra, and lepton momentum spectra. In particular the distribution of decay widths for the 2"- states D_2 and D_2"' varying along with mixing angle are presented. (orig.)