  We examine the potential of the $ep\to\nu_{e}q\gamma X$ and $ep\to\nu_{e}qZX$
processes to search for the anomalous couplings of $WW\gamma$ and $WWZ$
vertices at the LHeC with the electron beam energy of $E_{e}=60$ GeV and
$E_{e}=140$ GeV. The difference of maximum and minimum bounds on the anomalous
couplings, ($\delta\Delta\kappa_{\gamma}$, $\delta\lambda_{\gamma}$) and
($\delta\Delta\kappa_{Z}$, $\delta\lambda_{Z}$) are obtained as ($0.990$,
$0.122$) and ($0.362$, $0.012$) without electron beam polarization at the beam
energy of $E_{e}=140$ GeV for an integrated luminosity of $L_{int}=100$
fb$^{-1}$, respectively. With the possibility of $e-$beam polarization, we
obtain more improved results as ($0.975$, $0.118$) and ($0.285$, $0.009$) for
($\delta\Delta\kappa_{\gamma}, \delta\lambda_{\gamma}$) and
($\delta\Delta\kappa_{Z}, \delta\lambda_{Z}$), respectively. The results are
found to be comparable with the current experimental limits obtained from
two-parameter analysis at the lepton and hadron colliders. It is found that the
limits on the anomalous couplings ($\Delta\kappa_{Z}$, $\lambda_{Z}$) through
the process $ep\to\nu_{e}qZX$ at the LHeC can further improve the current
experimental limits.
