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We calculated the harmonic spectra generated from the asymmetric molecules of HD+ and HeH2+.It is found that HD+produces only odd harmonics,while HeH2+ produces both odd and even harmonics.Further analysis reveals that for both HD+ and HeH2+,the nuclear dipole acceleration can generate even harmonics,but it is three orders of magnitude lower than that of the electron.Hence,the electronic dipole acceleration dominates the harmonic generation.For HD+,the electronic dipole acceleration only contributes to the generation of odd harmonics,but for HeH2+ it contributes to the generation of both odd and even harmonics.Besides,one concept of the broken degree of system-symmetry is proposed to explain the different odd-even property between the harmonic spectra of HD+ and HeH2+.