The inelastic phonon scattering of one-dimensional electrons is analyzed by a diagrammatic technique. The contribution of the maximally crossed diagrams is evaluated for ${\omega }_{\mathrm{ph}{\tau }_{\mathrm{ph}\mathrm{\gg }}}$1 and ${\omega }_{\mathrm{ph}{\tau }_{\mathrm{ph}\ll }}$1, where ${\omega }_{\mathrm{ph}}$ and ${\tau }_{\mathrm{ph}}$ are the phonon frequency and the inelastic relaxation time, respectively. The dependence of the conductivity upon ${\omega }_{\mathrm{ph}}$ and ${\tau }_{\mathrm{ph}}$ is found. In the ${\omega }_{\mathrm{ph}{\tau }_{\mathrm{ph}\ll }}$1 limit, the scaling result of Abrikosov and Ryzhkin is reproduced.

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