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The Lα, Lβ and Lγ x-ray production cross sections of Dy and Sm by electron impact are measured at energies from near threshold to tens of keV. In the experiments, thin targets with thick substrates are used. Meanwhile,the electron transport bipartition model is used to eliminate the influence of electrons reflected from the thick substrates on measurements. The measured x-ray production cross sections are also compared with the theoretical predictions by Gryzinski and McGuire.